Be sure to let Java run, otherwise the game won't load! If you are having trouble starting the game, add the following sites into the site exception list in your Java Control Panel (JCP).
To change your username, click on at the top left corner and enter a new username. You can play online but can only join 1.5.2 servers.
Once you've joined a server, register your username by entering '/register password password' without quotes to be able to play. Obviously, pick a better password than 'password'. You will need to do this for every new server you join or every new username you choose.
To play fullscreen, click on Options > Video > Fullscreen: ON. You can also press ESCAPE in-game to get to the options. Just toggle Fullscreen: OFF when you want to stop playing.