It's against the rules for districts to train possible tributes. One and Two always do it anyway -- the Capitol looks the other way because they like them and the districts don't call it that. Four usually sends trained tributes and they're in the pack.

They'll pull in others, too, if they're impressed during the four days training the Capitol gives us. Someone exceptionally strong or smart or fast. If they look like they'll benefit the Careers long run, they're offered a place in the pack.