That really depends on how much you want to edit your clips. If you want to keep it easy you can put music under it with any video editor and put a color correction in YouTube. (yes, that is possible)
I've seen alot of people use Sony Vegas. It isn't free, but it's easy. Excelent tutorial
for this program.
If you want to use more advanced programs you could go with Adobe After Effects but I don't suggest you do that since you asked for easy editing software.
If you really
want to keep it basic you could mess around a bit with Windows Movie Maker. It can be used to put clips in the right order, putting in some music, etc. All the basic stuff.