Well, if we're talking the KGA here (2. ...exf4) then White's most common continuations are 3.Nf3 and 3.Bc4. These variations are covered in the diagrams below...
For the 3.Nf3 variation, the Fischer Defence 3. ...d6 seems to be pretty strong. The idea behind this is to go for the continuation 4. d4 (or possibly Bc4, but it's probably not as good) g5 5. h4 g4, kicking the knight backwards because the pawn on d6 guards the e5 square, preventing the knight from advancing. Black can then use the two advanced pawns on the kingside to pressure the White king and go for an attack.
For the 3.Bc4 variation, a possible continuation is 3... Qh4+ 4. Kf1, which immediately prevents White from castling but allows White to gain a tempo later with an intended 5.Nf3 poking the queen away. Note that while White is unable to castle, the king's position is still reasonably secure in this variation, and it is not always easy for Black to attack it...it's probably the main idea for Black in this variation though, since the queen and pawn are able to put pressure on the kingside.
At the highest levels the KGA yields a good number of victories for black and very few draws. But, I can't seem to understand black's overall plan here. White is rushing development and ideally trageting the weak f7 square. Besides defending a mate and holding the pawn to use for a future advantage what are black's strategic goals in the KGA?