These are the same instructions from the thread, mirrored here for your convenience:
1. Go here and submit your SC2 name and code in the following format: Name_Code (e.g. Harris_788). No need to register a challonge account or anything, just click 'sign up for this tournament without a Challonge account.' This will enter you in the bracket.
2. On this page, connect to chat using your SC2 name and code in the same format as above (Harris_788). Find your next opponent on the bracket below the chat and set up a game with them on the appropriate map. The map to play for each round is listed in the thread.
3. After your game, upload your replay here and report the winner in chat. In order for your win to be registered, you must report it. Go to step 2.
Full screen bracket