Instructions
Head to Twitch.tv and register for an account (see Resources). Your username will be the name of your channel, so think carefully before committing.
Focus on PC games. You cannot stream PS3 or Xbox 360 titles without an external capture card, while you can stream directly from your PC without additional hardware.
Download and install Open Broadcaster Software or FFSplit (see Resources). Both are free software platforms built for games streaming.
Log in to your Twitch.tv profile, and head to ̶0;Twitch.tv/broadcast.̶1; Copy the stream key provided.
Paste the key into the appropriate settings panel in either OBS or FFSplit.
Set up your stream by adding game capture and audio capture from your headset or microphone. Stream when ready by clicking the "Start Broadcast" or "Start Stream" button. The application will automatically stream to the channel associated with the key you saved in the options screen.