When you have logged into the game you are presented with the Lobby. It is split into two panes, left and right.
On the left side there is a list of all ongoing ("active") matches. If you press the "old" button you will see a list of finished games. Each match has an icon that explains what state the match is in:
|Someone wants to play with you!|
|You have sent this invite|
|You can do moves in this game!|
|Waiting for the other player to move|
|You won this game!|
|You lost this game|
|This game was a tie|
|This game timed out|
The first time you log in this list will be empty, naturally. To fill it up you will have to start challenging other players (or wait until someone challenge you). This is what the right side of the lobby is for. Depending on what tab you have selected this list can either show a list of the top players of clairvoyance ("top"), or a list of recommended and saved foes ("foes"). "Recommended foes" are selected based on their likelyhood to be good and interesting opponents. "Saved foes" are players that you have decided that you want to have easy access to.
To find a certain player that you know the name of, just use the search function. Enter the username (or a part of it) and press enter.