Video chatting doesn't require any additional software, but only some browsers are supported if you're chatting from your computer.
Most Android devices can use Hangouts too, accessible through Google Play.
Once you choose a contact from the Hangouts app, you'll see options for starting a video or audio call, much like when using Gmail for internet calls.
They have added the video chat option very recently.
Omegle allows you to share the chat log in your Facebook account or to download it to your PC. It allows you talk to your friends or to random strangers.
If you find a contact you want to chat with, you can just click their name to bring up a new chat window on the bottom of the Gmail interface.