You have to walk around the cities and highroads and press 'square' to open up their Blitzball info. If they play, and don't already have a club, you can sign them, if you can afford them. Bear in mind that not all people play Blitzball, you just gotta find the right ones.
The best place to start looking immediately after the first tournament is the Luca docks, where the stadium is. There's a big Ronso on dock 1 who makes a great forward. There are a few security guards, like 'Biggs' and 'Wedge' who make good players too. Oh, and the news reporter Shaami is it? Quality striker!
Personally, I prefer to keep the same team and build it up, coz then it feels so much better inside...Ok, it doesn't...Sign everyone you can!