I want to make a video chat website that I can use to chat with other people. How can I do this?
I answered this question a while ago, please take a look! To sum it up, if you want to do it right you need to setup some specifications. Will it use flash? What features must it have? (I.e login, logging conversation, report user module, match making)
Typically, detecting and presenting users via their webcam is done in ActionScript, which will produce a flash file. You can do the chat in action script as well, however I would do it in PHP and Ajax to retain a little more control. There are plenty of open source projects you can glance at, to get a feel for how to do things.
As I mentioned in my previous answer however, video chat sites are ubiquitous. Don't waste time reinventing the wheel. The only real reason I can understand for creating yet another video chat site is to apply your knowledge in whatever language. Unless you have a ground breaking idea, I wouldn't expect it to be a big hit. In the case that you do have a big idea, don't post it - Just do it (:
If you're only developing this project so that you can video chat with your friends, consider using a service such as Skype.