Download FRAPS from www.fraps.com (go figure) you'll only be able t record 30 seconds at a time unless you pay $37. I''s a start, but you can record at any point by just pressing a key.
To make a good movie, First make a track, then edit the camera angles, that way, you get the procision that you get from the cockpit, but at the same time, you can get external shots.
Like what scott said, first run a mission do whatever you want to be in the video but be sure to record it as a track before you go on the mission. After its done it will ask you to save it, and run it again but this time use the camera angles you want. Here's some tips with camera angles Shift-j will have that jiggle effect. It's just one of several clever camera tricks you could use. For example the F2 external view, you can do a different type of zoom with ctrl / or *. You can also use free cam ctrl F11. You can padlock it with the . from the numpad key. One of the main things you will see in other lock on movies is the use of the F4 view, this is pretty hard to master because it requires you to change the code in one of the files. Lucky for us there's an easy way and thats downloading a program called LoCFG. It not only helps you tweak lock on but theres an option in there to change the f4 view. Normally the f4 view is facing your 6 and it rotates around that axis. By changing it, we can place it anywhere like under a pylon, above...etc. Another trick you can use is in the F2 view, you can circle around the plane, then use shift-esc to unlock the plane so you can look around from that axis. It's pretty complex, hope you get it.
Then play it back but capture it with fraps
Then edit it with a software such as Vegas 6.0 (the one GA uses).