Glance over at your cell phone. How does it look? Dirty? Smudged? Now think about putting that phone up to your face to talk, or touching it with your hands to text. Are you now sufficiently motivated to clean it up? I'll tell you how when you read on.
Supplies:
• Isopropyl Alcohol 70%
• Q-tips
• Microfiber cloth
• Screen protector (optional)
The Method:
1. Turn off your phone and let it cool down.
2. Remove your case.
3. Clean the casing and buttons with a cotton swab and alcohol.
I prefer to use undiluted rubbing alcohol because it evaporates quicker than an alcohol:water mix. Less liquid means less chance of damage to your phone.
4. Polish your screen with a microfiber cloth.
Never use any liquid on the screen because it could damage the protective coating of your phone.
If you want to give your phone a bigger makeover, treat it to a new protective screen film. Applying one of these can be tricky, but taking your time and using a credit card or flat tool to push out air bubbles will help it adhere perfectly. Here's a more detailed description. 
5. Clean your case.
You don't want to put a clean phone back into a dirty case, so use the same method to refresh your case. Make sure to polish the inside to prevent trapping dirt, especially if you have a transparent case like I do.
6. You're done! Reassemble your phone and enjoy.
(Images: Jennifer Hunter)
8 Secret Spots to Hide Valuables at Home
The Live/Work Studio of Robert Siegel Handmade Ceramics
Good Food to Share 
The Big Book of Small, Cool Spaces 
Apartment Therapy Presents 
The Eight-Step Home Cure 
Howard Butcher Bloc...
10 Easy Vacation Meals to Feed a Crowd
Recipe: Chopped Brown Rice Salad with Grapes and Pecans
I just use an anti-bacterial wipe on mine.
Be aware that using alcohol to clean your screen can damage or remove the oleophobic coating that Apple puts on to reduce fingerprints.
How is putting a phone up to my face that got smudged from my fingers any different than touching my face with said fingers..?
I just use regular alcohol on mine and a normal cotton ball. I do this nearly every day and during flu season and it's never damaged my phone (nearly 5 years old, now.)
It also works fine on the silicone cover I have.
But I'd think doing a test site on the screen might be a good idea though, maybe with a cotton swab.
I don't use a case and I never clean it. Turns out, the cellphone still works! Problem solved.
Sorry this is bad advice. Apple's own website suggests against any abrasive cleaners since it has a unique coating on the top of the glass that can be compromised.
"Don’t use window cleaners, household cleaners,
aerosol sprays, solvents, alcohol, ammonia, or abrasives to clean iPhone"
I use eye glass cleaner I get at the drugstore. Of course I don't spray it directly onto the phone, but on a microfiber cloth first. I always have a screen protector on my phone so using whatever I want on it is no big deal. I'm on my third iPhone and so far no problems. I think not using some kind of mild household solvent is unrealistic. Your face and fingers are oily and sebum is pretty destructive on its own. Look at the arms on old wood furniture and you'll see what I mean.
Monoprice has iPhone screen protectors for under $2 a piece. I was almost mad when I found them because I'd been paying upwards of $12 before. I think they have plastic protectors for the back side of you phone as well.
On current phones that use Gorilla Glass for the screens, a screen protector is not really needed (unless you are really hard on your phone).
To add to the anti-alcohol comments, 70% alcohol IS a mix of water and alcohol, which is why it is labeled 70%.
Also, there are alcohol-free cleaners for LCD screens that may be more suitable for cell phones, particularly the screens. The difference being this cleaner won't yellow any plastic parts over time whereas the alcohol does.
Okay folks, just to clarify my instructions, clean the casing of the phone with alcohol and clean the delicate screen with only a microfiber cloth. Sorry for the confusion.