The buds, greyish brown bark and pink petioles look exactly like a Japanese Maple (a.k.a. acer palmatum) of mine which is doing the same thing right now.
Check this site out:
http://www.bonsai4me.com/SpeciesGuide/AcerPalmatum.html
Don't worry if the leaves on your tree (assuming it is a maple) do'nt look like anything like the few leaves you see on that site, there are well over a hundred different varieties.
You definitely want it out of that moss. If there's a large garden center near you you can sometimes find small bags of bonsai soil in a pinch. Otherwise you can order some from one of the many online retailers (who can also provide a pot, accessories and a book or two).
EDIT: I just noticed you're in Maryland, if you're in central MD check out Homestead Gardens in Davidsonville (I'm not affiliated). They have enough to get you started.