You can download the "Wtv client" from this link.
If you don't have an account, register a new account at this link.
As you can see on the image below, when you download the WTV client, open it, type your username and click on connect.
Picture 1. Connecting to WTV!
As you can see on the picture below, when you connect you will get a list of all games available, select a streamed game that you want to watch from that list.
Picture 3. Selecting games!
After you selected a game, open Warcraft III, go to LAN and join the game you selected, as shown on the picture below.
Picutre 6. Rehosting Game in Chat!
Now that you have joined the streamed game, you can enjoy it.