Oberyn Martell fights for him. He fights the Mountain (the Hound's brother) and while Oberyn starts out winning, he tries to get the Mountain to confess to raping and killing his sister but when he does, the Mountain ends up getting the upper hand and killing Oberyn. Jaime then breaks Tyrion out of his cell to help him escape but before he leaves he decides to visit Tywin. Tyrion ends up meeting Shae and he asks why she betrayed him. He ends up killing her. Finally, he confronts Tywin and ties up all his loose ends. After a long conversation, Tyrion kills Tywin with a crossbow bolt and escapes Kings Landing.
Eventually he makes his father poop himself, though I don't know if they'll put that part in the series. Books 3 and 4 are really stupid.
Hopefully in the TV series they just start making stuff up. I think the problem with the books is that the author kills off all of his good characters and can't seem to ever replace them with ones you care about.
The same thing will happen with the TV series if they let it...
If you want spoilers then here they are for material which will probably be covered in the rest of this season
SPOILERS. The court has Gregor Clegane, the Mountain-That-Rides, fight as their champion. Tyrion gets Oberyn Martell to fight for him. The Red Viper does so in order to get revenge on the man who murdered his sister. He fights an epic duel with Clegane, outsmarting him and mortally wounding him. But before the Red Viper can deliver the final blow, the Mountain manages to grab him and crush him to death. Tyrion is thus found guilty and sentenced to death. However, Jaime forces Varys to break Tyrion out of jail and smuggle him out of the city. As they are leaving through some secret passages, Tyrion goes down one and emerges in his father's quarters. There he finds Shae in his father's bed. Angered, Tyrion strangles her. He then goes and confronts his father in the privy and shoots him dead with a crossbow. Varys then has Tyrion smuggled out of the city
*SPOILERS* Cersei names The Mountain as her champion and Prince Oberyn fights for Tyrion to get the chance to kill his sister's murderer. Both of them end up dying, but Oberyn is technically the loser because he dies during the fight. Jaime and Varys break Tyrion free before his execution and he kills Tywin and Shae before escaping the city.
So Tyrion, finding himself in a clusterf*ck, requests combat by trial.
Who will fight for him? Will they allow Jaimie to represent him in battle? And if Jaimie does fight, will Tywin allow his beloved son to die? If he shall die, he may have lost a hand, but after all, his fighting skills remain extraordinary.
Will Bronn fight for Tyrion? Honestly, i've never seen Bronn lose a fight, but i really do wish to see how he'd do against a Kingsguard. Could the end of Bronn be coming?
What i'd really love to see, is Bronn taking up on one of Kingsguard (could he fight Jaimie?i think he'd win against him, as he's the one who trains him), and shredding them to pieces. So that Tyrion earns his freedom and Cersei-Tyrion goose chase starts, one trying to kill the other.