Some games have in-game video capture options. The Sims 2 has a movie mode, and you just point the camera and click to record. The Movies also creates movies as part of the game play, or as a sandpit option (filming separately from the game content). This is the easiest way to start with machinima - buy one of these games and get going.
Alternatively, there are programs that enable you to capture any in-game footage. It's dead easy - just start recording inside any PC game when you're ready. The other thing you can do is to capture video from your PS2, X-box etc by rigging it up to a TV card on your PC.
AviScreen Classic, which you can download for free from bobyte.com. It's totally free but doesn't record sound. The really good thing about this program is that you can customise what part of the screen you want to capture. This means you can miss off the HUD etc, so you don't have to bother cropping it later.
Fraps, which you can download for free from fraps.com. It's free for the unregistered version, which lets you record up to 30 seconds at a time and puts a small url watermark along the top of the video. Fraps can also record the audio of the game, making life that bit easier.
GameCam - the lite version is free and you can download it from planetgamecam.com. Game Cam Lite is still Game Cam, only simpler and without the extended features set. Game Cam Lite allows the recording of real-time in game movies with sound via hot keys or an easy to use in game interface and was designed to work with most DirectX 7, 8, 9 and OpenGL games. Game Cam Lite was created for individuals who simply want to record movies.
Leadtek Winfast PVR (TV card for PC). Record your PS2, X-box etc footage with this. Stereo sound as well. Includes a hardware MPEG 2 encoder for top quality video. Definitely the easiest way to capture video from games machines.
Leadtek Winfast PVR (TV card for PC). Pretty much the same as above. Cheaper, but will do everything you need.