I would use drawer separators (like from container store or similar), or you could cheaply make your own by cutting a piece of cardboard to the right size. That would keep clothes in neat little "columns" within each drawer.
Another tip is to set clothes sort of on end so that you can see a bit of each article when they are stacked (i.e., stack them from front of drawer to back, not from bottom of drawer to top). That way you can see what you have and grab what you need. If you make top to bottom stacks, you won't be able to see items and may end up with an unruly mess digging through the stack.

There is a great set of drawer organizers at IKEA (meant for the MALM, but work in others) for $10. They are great for baby clothes and socks. I also use them in the top drawer for diapers since we use our dresser top as a changing table.

I use baskets and then group like with like. One basket for pjs, one for pants, one for shirts, one for socks and hats, etc. You can use any container you've got lying around.

I fold my son's clothes in half (not more) so the piles are sturdier and you can see what everything is. Then I put them in vertically so I can put in a couple of stacks per drawer. You could have one stack for onesies, one for t-shirts, one for nighties, that kind of thing. Maybe the top drawer could be for diapers and pjs, the second for onsies and shirts and the last for bottoms.

It really helps to have some kind of box or basket inside the drawer like the examples mentioned above. Newborn clothes are so tiny and don't always stack well when traditionally folded. It's always a puzzle to reorganize the clothes as they get bigger to fit the drawer! Also I had a three drawer dresser and didn't need all three until my son was into the 18 months 2t sizes. I used the bottom drawer for extra diaper or toy storage.

We use a dresser too and I like it better than hanging clothes.

The real key, for us, is to only store in there what your little one can (and will) wear. If grandma pulls out a lime green shirt and burgundy pants, at least you know that it fits and is season-appropriate.

Also, we have 2 bins for the closet: one for the next size up and an empty one for things that are too small. If something is too small, you immediately have a place to put it instead of thinking that eventually you need to clean out those dresser drawers.

We have one big drawer for every day - right now, it's pants "rolled" up in columns on the right, long sleeved shirts on the left.

The other big drawer is for pajamas and specialty clothes: swimsuits, short-sleeved shirts, flannel-lined overalls, sweaters, vests.

We have 2 small drawers on the top. One is for socks, the other is for miscellanous stuff.

These drawer organizers seem kind of spendy, but they would do the trick.

I think it depends on how deep the drawers are. One thing we found helpful was placing boxes at the bottom of the each drawer. Basically, next season would go in the boxes or ugly gift clothes or anything not in use. Then the actual clothes you were using would go on top. I didn't need dividers because the remaining space was minimal.

I use rubber bands for cotton items like onesies, or even diapers, sleepers, etc. I group them by type of item.

I fold an entire outfit together: onesie, shirt, sweater and pants with the pants folded in half and wrapped around to make a little bundle. This makes it so easy to get him dressed in the morning, and my husband can just grab a bundle and know it "goes" (something he struggles with!)

For socks and smaller items I just use little boxes we had around the house, like shoeboxes, etc. put in the drawer.

When my littles were very little, I would keep onesies, pants, and basic tees in rows all in the same drawer. This made it easy to grab a whole outfit with out opening and shutting drawers while trying to find a match.
Now, I keep outfits together, which makes it easy for me (and dad, babysitters, and grandparents) to grab a set and go.
Also, make a habit of putting just-washed clothing towards the back of the stash- it helps everything get worn before the little one outgrows it!

I found that rolling clothes up into little sushie style rolls works way better than folding them. And then box dividers.

I just started folding and then standing my daughter's clothes on end, so it's kind of like a filing cabinet. You can see everything without digging and insert and remove clothing without disrupting too much. Works great.

I use IKEA Skubb boxes (I think they used to be called Komplement?). They are fabric boxes with zippers in the bottom and they fold flat when you don't need them. I sort little things like socks, tights, etc. into them and then fold other clothes in half only once so they stacks don't tip over. I also keep an empty diaper box in the closet to toss all too small clothes in. If you sell at consignment, you already have your "to sell" box ready to go next season!

We do the same as inkstainedwriter. I fold the clothes in half (even up to my oldest's 3T clothes) and then stack them in drawers in columns. But we've taken previous Ohdeedoh reader suggestions and now always put items away already paired in tops & bottoms (which helps dad out immensely AND makes sure we don't end up with all brown pants and gray shirts at the end of the week).

We have one drawer for PJs/socks/hats/extras, one drawer for outfits in the current size and season, and one drawer for "extras" that don't fit in a pair, as well as upcoming sizes and seasons.

I also use the IKEA storage boxes...they are great! My son is 2 yrs now...since he was born, I have reorganized his clothes a few times... switching things around as his clothes changed. For example, I used to have tons of onsies when he was a baby, now its jeans and pants. These boxes make it very easy! and they are CHEAP!

Skubb boxes are the way to go - they have little ones that work great for tiny socks, and little hats, and then bigger thin ones that perfectly fit folded and little bottoms.
http://www.ikea.com/us/en/catalog/products/60192633

We actually use them in all our drawers, they fit great, even though we don't have dressers from ikea.

Good luck!

These are the IKEA storage boxes I purchased recently. They are more child-ish than the others suggested.

http://www.ikea.com/us/en/catalog/products/50171749

The other ones shared are probably more multi-purpose for after baby gets older (which I hear happens rather quickly).

Wow! Such great ideas! I can't believe I didn't think to put outfits together. Thanks for all the responses!

We use something similar to Skubb boxes that we picked up at the Crate and Barrel outlet. We just use one in the middle to divide the drawer into three sections.

We divide by similarity; we prefer not to do by outfit because his clothes are as mix and match as ours are.

I have a wardrobe with three shelves, three medium drawers and then a three drawer dresser and in the three shelves we put shirts/pants/sweaters. Clothes may seem teeny right now but they get bigger fast!

Sleepers/sheets/pjs/towels go in the shelving part and socks/hats/mittens go in the three smaller drawers. You will definitely want a little more storage than just this dresser, but if this is going to be your go-to, I'd put the clothes of the moment in. I box anything he hasn't grown into yet or has grown out of.

I group by like items, not by outfits, but I use shoeboxes and clementine crates to keep the categories separate on the shelves in our baby clothing cupboard.

I too use drawer dividers. They're perfect for a large drawer containing tiny baby clothes and can be easily rearranged as the clothes change in size and function. My top drawer contains the very basics: onsies, footies, sox, underwear. I have jewelry divider in there that works wonderfully for containing the tiny sox! Middle drawer has basic "outdoor clothes" like pants, hoodies and hats while the bottom drawer has the "house clothes" as well as some miscellaneous items such as swimsuits.

I too prefer to fold in columns which makes everything easily visible.

I dont fold the clothes. I lay like pieces on top of each other. That way there is a pile of long sleeve onesies, a pile of short sleeve onesies, a pile of pants, a pile of shirts, etc. the piles stay organized a lot more effectively than folded clothes did.

We have three drawers for our two girls. I fold the pants in thirds and for shirts I fold in the sides in and then in half and lay them in rows not piles so I see the folded edges. This way you can see everything and neatly slide out what you need. I do a row of pants, long sleeve, short sleeve, sweaters and pjs. You can fit a ton of clothes in this way. Hope my explanation makes sense.

I have a box slightly larger than a shoe box in the center of each drawer, separating the drawer into three sections. The clothes then get separated by type (long-sleeved onesies, short-sleeved onesies, pants, shorts, socks, etc.). I do fold clothes, but since they're so small, they don't stay stacked very well, which is why it's nice that they're contained in their boxes.

I rolled the infant stuff (someone gave me literally 30-40 white onesies..ugh...so they got rolled and stacked). Now I just fold things and tend to just keep shirts together, pants together, etc. I need to get some baskets or something because the drawers are pretty deep. I'm really not a fan of the dresser but the closet is just too tiny to hang everything up.

I only really use one drawer for current clothes. I have a giant rubbermaid that we're storing all her outgrown clothes in (we already know we're going to adopt another girl so we're keeping them) and the other drawer is for her diapers.

I have top drawer for cloth diaper stuff and burp cloths, middle drawer for clothing, and bottom drawer for crib bedding and towels.

I really only need the one drawer for clothes and just made separate piles for the different types of things, with stuff folded no more than in half. So I have a pile of onesies, a pile of sleepers, a pile of tops, a pile of bottoms, and a pile of "outfits". I put the larger sizes on the bottom of the piles, and figure we'll eventually pack away the smallest things once they no longer fit.

I made a small fabric box to hold tiny bits like socks. If you have a sewing machine, fabric boxes are easy to whip up. Here's my fabric box tutorial.

Am I the only lazy one? I found that even if I kept everything neatly organized, my 2-year-old daughter would regularly pull things out, mess up piles, move things from one basket to another... so now, honestly, I just embrace it.

We do keep things organized by drawer (socks and washcloths up top, then pyjamas next drawer, then tops (shirts/sweaters) in the next, then pants/skirts in the bottom), but things are just chucked in anyhow, no folding. Everything's jumbled up but we know roughly where things are and aren't fixated on super-cute coordinating (kids can get away with pretty much any colour combination anyway). My daughter can help put laundry away because it's just a matter of getting stuff in the right drawer; I don't have to worry about her disturbing neat rows of anything.

The room still looks tidy when the drawers are closed and I don't waste any time folding tiny shirts that are going to be blotched from breakfast within ten minutes.

Learning from this apartment therapy post, I now "file" my daughters clothes. Long sleeve onesies, short sleeves, pants and PJs with diapers in the top drawer (still a total mess--we use cloth) and socks in a low, flat tupperware container.

I do the same, swordspoint. The girls love to empty the drawers out and put everything back, and their drawers are emptied out and rewashed so often anyway, I don't bother folding. When they get a bit bigger and their clothes are less fiddly, we'll start. When they were tiny I used the stacking flat unfolded items method.

I do the same as moxley2, with a bin in the closet for clothes that don't fit anymore.

In our six-drawer dresser, I've got: one drawer with hats, socks, lotion, medicine, bibs, misc., two drawers with clothes that fit now, two drawers with clothes the next size up, and one drawer with special items I'm going to keep (knit sweater from grandma, favorite shoes, etc.).
In the often-used drawers I don't fold anything, just group them in there by type (pants on one side, onesies and shirts on the other). Life is too short to fold baby clothes everyday.

I may be late in adding my comments but I'd like to contribute that I always rotate my sons clothes. After doing laundry the clean items go to the bottom of the pile in the drawer. I fold everything to make the most of the drawer space. In our case, we have a 5 drawer chest, I fold items in half. Top drawer: wash cloths, bibs, and diaper items. 2nd: most worn items, pants/jeans and tshirts/tops/onesies are all folded in half, sleeves tucked in. Everything in this drawer fits, too small items are quickly removed. My son mainly wears jeans so there usually isn't an issue of 'matching' or putting outfits together. But putting the freshly laundered items at the bottom of drawer ensures all are worn equally, and things are not forgotten at the bottom. Next drawer: pj's and heavy sweaters & sweatshirts, again rotated after laundry day. Followed by receiving type blankets and sheets. And the lowest drawer is odds and ends, toys and such that are not ready for the toy box, but these will soon be moved as he gets into the drawers and I'll likely need the space as his clothes become bigger.