Peeta joined the Careers because he truly loves Katniss, and wants to protect her, which is his only goal during The Hunger Games. Since Katniss' training score was an 11, the Careers dislike her a lot a lot, and want her far gone which is why Peeta decides he has to make sure that they don't get near Katniss' life being over. I luvvvvv Peeta!!!<3<3<3
To protect Katniss. The Careers were treating Katniss as their biggest rival (outside their own alliance) so they wanted to hunt her down and kill her almost immediately. Peeta told them he could help them find her. But in reality, he'd be trying to lead them away from her.
Because he thinks it's his best chance of keeping Katniss alive.
He sort of "fake" joins them, pretending to be a part of their alliance because he wants to keep Katniss safe. He and Haymitch hoped that out of the two of them, they could at least bring Katniss halaman awal safely, though int he end they both made it.