I want to write a Flash applet(or any other possible app) to embed in my website that will play part of a video (for example: from the 0:20 to 0:40). The video is in MPEG format. I'm new to Flash - any suggestions on how to get started on this?
Well, if you're new to flash (as the edit says;) ), this might be a bit too complicated to explain it all here, but what you'll need to do is write a custom flv player using NetStream, and make sure your flv's (or other video media) are hosted on a rtmp server (media temple has a cheap one if it's just for personal use) you can then call netStream.play(flvName, startPosition); and add a listener to stop it when it reaches the point you wanted to stop it at using a cuePoint.
There's an example here: http://www.actionscript.org/forums/showthread.php3?p=875934