Fraps, DXstory, MSI Afterburner. They will all do what you want. Record to a seperate drive other then your OS or Games drive for best performance. Plenty of tutorials on Youtube on how to set it all up. Give those a whirl and see what you are most happiest with. You will need plenty of free drive space and then some sort of software to edit your clips and neaten them up. No one likes raw unedited clips on youtube.
Personally I found Fraps to cause crippling gameplay lag when I used it on my system (although mine isn't the beefiest of systems) so instead I tried Playclaw and this was much better. It does the same thing as the other programs mentioned here but most importantly for me, caused absolutely no lag when playing the game. You can get trial/demo versions of most software (some may have a watermark placed on your videos to inidicate you're using a trial version, or they may limit you to only being able to record a certain amount of time).
I bought Playclaw for $29.95 (about £20.00) and think it's reasonably priced. I use Playclaw for screen capturing and it outputs it as an AVI file and then I use Sony Vegas Movie Studio to edit and convert it to a YouTube-friendly MP4 and then upload it.