Got to www.metamask.io and install the add-on (Firefox or Chrome)
Create a wallet (remember the password and save the seed)
Sign into Metamask (generally an icon in the top-right corner of your browser).
Go to the 'Do Battle' tab on the Mythereum site.
Click 'Join Game' if you see one available, otherwise click 'New Game' and wait for an opponent to join yours.