I would say that Windows Movie Maker is a good free starting point. I've only used Movie Maker so far and it get's the job done, but seems to be limited in the amount of control I really want to get to.
As you start to find it's limitations the you could consider
Sony Vegas (pro)
Adobe Creative Suite
Or if you are a Mac person I've heard people rave about Final Cut Pro.
I'm trying to switch over to Mac.
Another thing to consider is that you need to have a pretty beastily comp system setup.
Apple products were designed for video editors in mind.
Microsoft products you probably want at least a quad core processor, 8 or 16 GB of Ram, a decent 1GB or higher graphics card. And either a solid state drive or a high 7200 RPM hard drive.
My system is only half of those specs except for a I have a beast graphics card and I routinely make mistakes editing because the timing of the audio and video sequence gets all jacked up.