I don't know how much woodland planting knowledge you have, so pardon if some of this is sort of basic. The first thing is to be sure you can id what is a weed. You may want to wait until next spring before you do anything other than hand removal of weeds so you will have a chance to find out what spring ephemerals are present.

Many of the most interesting woodland plants bloom in early spring before the trees leaf out and while the sun can still get through. By June, they've gone dormant again. If you use herbicides Indiscriminately, you could kill some wonderful (and expensive to replace) plants such as trilliums, spring beauty, solomons seal or mayapple. In the meantime, you can start pulling out obvious weeds like oak and maple seedings, garlic mustard, ivy etc. that are pretty easy to remove by hand. And start thinning out the feet of leaves so old plantings can pop back up.

Also I would make a drawing of your yard and note how much sun (dappled shade, dense shade, a few hours of morning sun, etc.), for each month for each part of your yard. This will be a good guide for fall and spring plantings later.

Look over the trees and see if you need/want to limb up any trees to open up dense shade to open shade so areas would become plantable. Or are there trees that need pruning because there are cracked branches or rotted trucks?

You haven't given a location or a zone, so it is hard to offer an recommendations for plant choices. But first what is already present and then what do you like? Do you want to stay with shrubs or do you want to make a few retaining walls and add some perennial beds? Do you want to add fragrance and/or plant for wildlife?

Are you going to be willing to blow your leaves clear at the end of each fall to some place at the bottom to turn into compost maybe or are you going to always leave them lie where they fall? If it the last, forget doing perennials and stick with tall shrubs.

And lastly, perhaps the single biggest governor of your plant choices: do you or will you have a deer issue?

That's your primer and should keep you busy for a while. Feel free to post photos of plants for IDs either here or in the Name that plant forum.

Kimka gave you good advice above, but be careful about removing fallen leaves - they nourish the soil and its inhabitants and help prevent erosion on that slope, as will the plants you decide to install.

The deer issue is a big thing to take into consideration. There are lists of deer-resistant plants.

I highly recommend checking around your area to see if there are any public gardens that feature native/woodland plantings. A few that come quickly to mind in the area are Mt. Cuba Center in Hockessin, DE; Bowman's Hill Wildflower Preserve near New Hope, PA; Leonard J. Buck Garden and Duke Farms, both in Somerset County NJ. Many of these will also have information to assist your endeavors.

Agardenstateof_mind is right about checking out public gardens. Longwood Gardens has some wonderful natural woodland areas too.Take a look at some well done woodland landscaping from very natural to more formal to get ideas of what you might like your finished yard to look like.

Notice Agardenstateof_mind I said thin out the leaves, not wholesale remove. If this was indeed a highly planted landscape at one time, there may be a lot of interesting plants under the masses of leaves. Bsilberz, I would look for signs of beds and do patch thining to see what pops up in those spots.

Are you near Baltimore?