What should I do to cover them so it looks nice? I've never done anything like this before and I don't wont to ruin this thing. Any ideas?
It really depends on how you feel about preserving your rifle. You'll hear everything from "strip and refinish - it's your rifle" to "don't touch it, put it down, it's part of history, leave it alone".
Personally, I would, at a minimum, touch it up would a cold blue solution like Birchwell Casey's Superblue. Dab it on with a Q-tip and buff it with 0000 steel wool. Repeat several times until everything blends together.