There is a button on PBW for listing all currently open games, but don't expect many players to join just through browsing that. All the games I'm in were announced on this forum, which is the best way I know of to get people to join. There's also a forum on PBW where new games can be announced, but very few people check it. There's another forum over on
spaceempires.net that gets a bit more traffic, but it's still a poor second to the Shrapnel forum.
If you're looking for a game to join yourself, the easiest way to get in a one-on-one is to notify Alneyan that you'd like to join the
King of the Hill League.
This thread would be a good place to do so. For larger games, you'll either have to be very patient - they don't start up very frequently and generally take a while to gather players - or find one in need of a replacement player and take over for the person that quit. If you don't mind playing with a major mod, The Galactic Invasion 2 game (alphabetized by "the") needs one replacement at the moment. I believe that particular empire is set up as a nomad race, which is a very different play style from stock, but it's a cooperative game against two space monster races so you shouldn't need to worry about someone trouncing you while you're still learning how things work and making up for all the missed turns.