If you're new, the Lobby is a great place to get started.
Find the room you're interested in, type in a nick and get started chatting! Pick a room by geographic region or by topic of interest.
Created by a Russian school boy, Chatroulette connects millions of strangers in random video conversations.
The web app itself is pretty bare-bones, with two video panes showing the user & you, a huge pane for text chat and a couple of buttons for controlling the chat.
Each random chat conversation is referred to as a game and you can restart a new game at any time.