If you are using a windows based pc, they used to come with a program called windows movie manager (or maker). This works pretty well for anything that just needs cutting a splicing, and possibly color corrections. If you are using windows, I would suggest starting with this program as it is mostly drag and drop. If you wish to get more into the professional side, there are many good choices out there.
Personally I use Sony Vegas. I cannot recommend this program over others because I haven't used any of them. One of my previous computers had Vegas on it, I learned how to use it and kept it. Check with YouTube on video editing, there are a lot of great helpful how to's.
Casey