The first time that you start TwitchOverlay, you'll be greeted with a screen similar to this one.
Start off by putting your Twitch username under the "username" field. Now we need to get an oauth token to finish connecting.
As of Sept. 17, 2013, Twitch now requires that you log into IRC using an OAuth token instead of your plaintext password or hash for additional security.
An oAuth token is needed to connect to Twitch's IRC (Internet Relay Client, or just "chat") server.
Go to https://twitchapps.com/tmi
Click the "Connect with Twitch" button
At the authorization prompt, click "Authorize"
Copy the textbox contents under "Use the following password to login to chat
Now that we've got the oAuth token, we can log in to TwitchOverlay. Press the "Log in" button to do so.