I don't recall a tutorial, but quick basics -- from the main page, there will be a menu on the upper left of the screen. Clicking "Play Now" takes one to the main game lobby, which shows player's favorite games and all currently available games. Games are organized by player's favorites, followed by all games. In each group, games are organized first by realtime games (green background) and then by turn-based games (yellow background). These can be shown/hidden based on the check boxes at the top right of the table listings (underneath the list of player's favorite games).
To join a table, click on it. You will then be able to see details about the game such as who is at the table, game speed, rules variations, etc. Actually, most of these are available from the summary page as well, but you'll get more information about the players currently around the table, such as declared country, language proficiency, disconnect/timeout tendencies, etc.
To actually join a game, click the "Join Game" button on the left. Before the game starts, all players will have to agree to actually play the game to the end (which is why leaving the table is noted as a penalty on this site).
Once the table administrator starts the game and all players have agreed to play, the game is set up. From there it depends on the actual game what the interface is. Generally, hovering over an object provides help about it, and clicking on it does the standard play for that object (putting a card on the table, selecting a token to move, selecting a die to roll, etc.)
Hope that helps.
