Pull it out of the ground and start fresh.

looks like an overgrown juniper. Not much you can do to "trim" it at this point without making it very ugly. Replace it.

The brown is likely because it has outgrown itself and those areas cannot get the proper lighting they need. Juniper is more like a cedar tree than a bush and will grow thick and woody. To tame the beast, simply cut it back. It's been there long enough, no matter how far you cut back it's going to return. These evergreens tend to grow outward versus upward. With a little TLC this beast can be kept looking nice.

It's a spreading juniper that hasn't been properly pruned. It would take considerable time to get it back under control and looking good. You would be better off removing it and starting fresh.

Pulling it out of the ground is certainly the fastest way and it's far from easy (if you go through the trouble of actually getting the roots out as well) but I think that's the lazy way. If you do that, you haven't learned anything about how to care for the next plant you put in the ground. Looking at the state of the grass (i.e. nonexistent) between the tree and your home, you've got a challenging area to work with, so it's not like you can just pop down to the nursery and expect to build your dream landscape.

Instead, cut from the inside to thin it out. Cutting the outside will only reveal the leafless inner branches, as you've discovered. Take out between 30-40% of those inner branches and the shrub will pull back and regenerate from the core. Then snip off the very tip (1-2 inches) of the remaining branches to stop them from getting longer. The best time to do this is late in the winter, before spring growth begins. Expect the process to take a full year.

Don't feel bad about ripping it out and starting over. Some plants are only attractive (or productive) as juveniles. Gardeners view such occasions as opportunities. Of course, if this were a rare and desirable hard-to-grown specimen it would be a different story. But it decidedly isn't.

It's hard to tell from your photo, but it appears to be either a Yew (Taxus cuspidata) or a Spruce of some unknown species ( perhaps a weak, Norway Spruce). My point is, if it is a spruce or fir tree, then there is not much you can do for the plant, and any attempt at rescuing it will only make it look worse. However, if it is a Yew, it is completely salvagable, as Yew's are the only needled evergreen that can handle hard pruning.

The great estates in France and England have enormous Yew hedges, which periodically require hard pruning back to the trunk or back to the thicker stems, to renew them. On my property, where I garden and where my parents and grand parents gardened, we have two long 100 foot yew hedges. Every decade or so, they need some heaving pruning, to keep them in scale, and out of the driveway. Here is how to do it.

First, properly ID the plant. You can send me a close up of the needles to my blog ( see my bio ) or, Google Growing with Plants, and you will find me.
If the needles are rubber and dark green, and if the shrub sometimes produces little mushy red berries, then it is a Yew ( the latin name is Taxus), but most nurseries will sell them as Yew. It is not a juniper species from what I can tell from your photo.

There are many species and selections. If it is a Taxus, I would cut half of it back hard this year ( now is best) and then the other half next year in the spring, before growth starts in March, if you live in USDA zone 5, which is what I am guessing.
Yews can make awesome sold green/dense domes, globes, or conical shrubs if clipped once a year. Or they can grow into a tree, and kept shapely with a little pruning. They can live hundreds of years.

I think you might want to take onto consideration the mature tree it is growing under, before you consider pruning vs. removal. Digging in to remove a dense football that close to the other tree (oak?) is risky. If you cut the evergreen to the ground without removing the roots, you have an eyesore. So it is worth salvaging, yes?

The suggestion that it may be a yew is interesting. The placement of the plant makes it likely, but the shapes of the branch ends look wrong to me.

Hire a certified arborist to prune it. They will identify it for you, assess its health, and prune it into a better shape. It's hard to plant under large trees because they suck up all the water. If you have an established plant that can coexist with it, I'd be inclined to keep it.

Also, I will add a few more comments after reading what others have suggested.
First, DO NOT trim an evergreen from the inside, towards the outside. This is fine for opening up a deciduous shrub to reveal muscular or attractive branching, but unless you want to 'open up this plant to see through it, it most likely has been growing too weakly to make an attractive branched specimen. I would trim the entire plant back to a shape, either a natural form, and allow the old wood to let the dormant buds re-emerge. Yew are the only everygreen to have dormant buds hidden in old hard wood. They are best grown into formal shapes, or carefully tended to look like a natural, dense form. Once your new growth emerges after a hard trim, you can then thoughtfully edit the tips of errant branches to what ever shape pleases you.

Sure, it will look bad for the first year, but in another years time, it will look magnificent.
You have no grass because of the oak tree, and it's shallow roots, not because of the Yew. One reader mentioned your poor or lack of a lawn. I would simply blame that on the Northern Red Oak ( Quercus rubra), that I can see in the foreground. Though they make fine landscape trees in the large landscape, if you want a nice lawn, this can be challenging given that mature trees have significantly aggressive roots near the soil surface, they can even lift the pavement in parking lots.
You may want to consider adding a new layer of topsoil ( 6" or so) over the rootsm but reduce it near the trunk. The second reason you have no lawn, is that the shade from the Red Oak is denser, often so dense, that its own acorns find it difficult to sprout. In the end, you will need to decide what is more important to you - a lawn, a mature oak, acorns, or some time to let the over grown yew find its old glory. Of course, you can remove them all, and start again, but that is up to you.

MMattus - what kind of shape are you talking about - like those crazy hedge gardens some people have with animal shapes and whatnot? Please be more specific I am curious.

“Knowing trees, I understand the meaning of patience. Knowing grass, I can appreciate persistence.” - Hal Borland.

For your tree, I agree, a hard pruning will bring it back to life and give it a nice shape. If you haven't pruned before it is worth it to hire an arborist the first time and have them teach you. You will be rewarded in a year. Deferred gratification is so underrated these days.

Start over.

Looks like juniper or cypress to me. Juniper performs best in full sunlight, and the area in the picture looks shady now. And all these are not "forever" shrubs. (Boxwoods and yews are probably the longest living and easiest for transplanting).

I'd clear it out and re-do the area. Perhaps a combo of yews (or lower-growing boxwoods) and some flowering shrubs? Or a patio-like are in the shade?

Mature trees, if they don't overgrow a house, are an asset and can cool an area up to 10 degrees in the heat (depending).

Have fun! A garden is never done. :)

I was going to say "get rid of it" but then I realized that it gives you privacy.
I would start by trimming it hard and waiting a year - you will probably be rewarded with a much nicer looking tree next spring. If trimming ruined it, then go ahead and remove it next year.
I would plant something in front of it to hide it. You'll have to plant at the edge of what can be seen in the picture because of that big tree. Maybe some Rhododendrons? Check a local nursery for some shade tolerant shrubs that can be planted under large trees (Note: In most of the country, July is not a good time to plant shrubs, you might have to wait until the fall or next spring).
Raking out all of those leaves and planting some shade tolerant ground covers (no grass = less mowing) will make a big difference in the way that corner looks.
@Parnassus has the most valuable advice - patience!

Many evergreens cannot be pruned past the green part. If you prune into old wood they will not sprout out again. You will be left with brown dead looking branches. It is also very difficult to prune a weeping tree and have it still look presentable. You might be able to cut off the part leaning on the building if you reached behind and left some greenery weeping in front of the cut off part.

The questions I think you need to consider are: is it giving you privacy or blocking an unwanted view, is it taking up space you want or need, do you need some greenery to look at during the Winter, do you like it?

It will be difficult to grow things under the large deciduous tree with or without the evergreen. You could keep it and try to play up its weirdness of shape. You could make a little island of evergreen groundcovers and plants that don't mind dry shade. Some spring blooming plants and bulbs might do well planted amidst the groundcover. If the evergreen gets some sun in its upper branches, you could coax a clematis to grow into it. You would need a good size hole filled with healthy soil and careful watering until it took off.
The large trees cramp your choices but on the other hand you have inherited something magnificent that it would take a lifetime to replace.

I agree about keeping it for the sake of privacy! Or to cover up something unsightly in the neighbors yard. Give pruning it a try, you can always remove it later.

Cut it down. You won't be able to make it look nice. I have the same problem with an overgrown evergreen on my property. The townhouse across the street had the same landscaping had hers removed. She planted a couple lovely birches in its place.
Privacy is highly overrated unless you're planning a threesome with the fitness instructor from your gym or are doing some experimental planing of cannabis. But if you *must* have privacy, just about anything would look better than that monstrosity that looks like it lost its primary apical meristem and can only grow out instead of up. Chop it down, start a bonfire and dance around the flames naked. Before long, your neighbors will erect their own privacy screen. Problem solved.

Damn, I really need an edit feature.

@KHINNJ Best answer...I was just going to say, chop it up and out of your yard......; 0

Joannaelizabeth - to answer your question, the shape you can end up with is up to your style. You may want to consider starting over again with some new shrubs to save time, and to get the perfect design that you want.

If it is indeed a Yew, and if you want to save it - I would cut it back drastically this year, and allow it to re-sprout. In early spring, snip back the new sprouts which will be about 8 inches long before the re sprout - this will allow them to grow even bushier. As for the final shape, I can't tell what your garden's style is, or what you prefer - if you want some ideas, write me at my blog, and resend me some pics - I'd be happy to suggest some alternatives.

You can either opt for a more natural form, allowing the new growth to branch naturally with a careful nip and snip here and there to keep the growth bushy, or, trim for a dense form, either a globe, a cone or even a peacock if you are handy with snips.

I would suggest a natural globe form, Yew can be trained either into formal shapes, or informal ones. Left alone, a new shrub can form a nice multi-branched tree, the way it grows in the wild, but most gardeners prefer a denser, more architectural form. It will take about three years to get a nice globe-like shape, that is, if it is getting enough light.
I would also fertilize it twice - now, and again, in late winter with an granular fertilizer with an analysis for needled evergreens. Fertilize only just this first year - most evergreens will not need fertilizer, but you do want a full burst of new growth this first year.

Chopping it up is an option, since new yews are inexpensive! But no need to dig out roots, just cut close to the ground, and prepare a new hole with organic material since your soil looks like sandy clay to me ( given that the oak tree is growing so well!).