Under the section Play or Watch Bridge click on the line, List all tournaments. You will then be shown a listing of Tournaments starting soon, with all different types of tournaments, ACBL, BridgeBase Masterpoints, Robot tournaments, Free tournaments, and the last listing, All tournaments.
Notice the group of buttons above the listing of tournaments, Pending, Running, Complete, and Refresh. The button in Red shows you which list you are reviewing. Beneath the listing of tournaments you can click on the "Substitutes" button when you'd like to be a sub and don't really care which tournament. This will add you to the substitute list where any tournament director can call on you to sub in any tournament. The Refresh button will renew the listing of games to add new games and remove games which have either begun or ended. To be added as a sub in a specific game, click the Join button on the tournament, and then click the "Substitutes" button.
But you're interested in playing so you will click on the Pending button and select from the list which type of tournament you want to play. You will then be shown a list of only those games starting soon that meet your criteria and under Status the amount of time remaining until the game begins. Clicking on the More button by your chosen tournament gives you specific information and rules on that game - what type, scoring, the TD, number of boards, how long it is expected to last, and other pertinent information specific to that tournament.
Now you have found a game you're interested in playing so you will click the Join button at the end of the line that describes your chosen game. This gives you another screen with a lot of valuable information.
First, on the left, you will see the partnerships already registered to play. On the right, you'll see a list of players who are looking for partners. Each of the names on the Partnership Desk will have specific information for that player. Clicking on the name of a person there will show you that player's profile and allow you to initiate a conversation with him. You can also simply add your name to the Partnership Desk. If you want to add your name, click that button (Add your name) and select your Payment Preferences if this is a game with an entry fee.
When you find a partner you think will be compatible and fun to play with, click the 'Invite' button following his name, he will be sent a system message telling him you want him as a partner, and if he accepts, both your names will be moved from the right Partnership Desk to the left, Registered Partnerships.
Of course, if you already have a partner, you will simply click the Register to Play button on the left, and type in your chosen partner's name in the popup window. He'll then be sent a notice that he's been invited to play and when he accepts, your names will be added to the Registered Partnership list.