Dark Prince: You simply enter the tournament. On BK people create their own tournaments, rather than them being created by the site. On the tournaments link, what you see are a list of open tournaments, the tournament name and who created the tournament. Most tournaments (like IYT) have multiple games types and you choose the ones you wish to play in. Not all tournaments have all game types and some are dedicated to one game type only. NB. with a pawn membership you may only enter 1 tourny.See posts below.

The League will occasionally create a specific espionage tourny and all are invited to play. The link shows a tourny already under way.
Sabotage Leauge - Small Fast Espionage - #1

You can also find games under waiting games. You can reduce the list by applying filters to this so so you can't see the Ludo game for example. Or choose new game and it will go into the waiting room.

There are also team touraments, which you play as part of a fellowship. Here is a link to one under way:
Jan 2009Cynophobia(Fast Espionage)(NO DAYS OFF)