I have a step by step process I use to make my own videos:
Acquire a demo. Either type "record <demoname>" in console or get a plugin like PREC to do it for you. I use PREC because I keep forgetting to do it manually.
Play back the demo in TF2 and convert it to video with a method of your choosing. Shift + F2 brings up a Demo UI that lets you speed up/slow down playback, as well as skip to specific frames. (Allegedly. Skipping frames tends to make my own copy crash.) You can use TF2's ingame recorder (.tga sequence or .avi) which tends to be slow but results in a higher quality video when you're done, or use video capture software like FRAPS. (Tip: Use the parameters "-window -noborder -width XXX -height YYY" in TF2's launch options to force specific screen resolutions and alleviate Alt-Tab woes.)
Edit the result in the video editing software of your choice. Note that if you record a .tga sequence, you'll need to use something capable of stringing them together like VirtualDub, even if it's just an intermediate step. Also note that .avi files may not play properly in media players until you've finished editing and encoding them, since the methods used to generate the video result in huge filesizes, which media players tend to freak out over.
Publish to YouTube or similar.