You can start a lobby by clicking on one of the lobbies on the Play Page.
Both are usually the result of a pop-up blocker or anti-virus software. If you can't or won't fix this, uncheck the 'Use pop-ups' option to open the lobby in the same window.
If everything is Ok, getting into the lobby will take only a few seconds. If getting in takes very long (e.g. a couple of minutes) there's probably something wrong with your Java installation, possibly multiple versions are active.
To solve this, reinstall Java properly.