What comes next depends on whether or not your opponent accepts the gambit. If 2...exf4, then 3.Nf3. As you probably know, you have to play Nf3 to prevent problems from Black's Queen. Now, if Black declines the gambit, the next move will defend the e5 pawn. If black pushes his King-side pawns to defend e5, you could end up with some interesting and sharp attacks. Many of the lines I've played with the King's Gambit have involved fighting on the King-side. As Black, you're going to have to invest a fair amount of time into building a good defense if you decline the gambit. As White, you have to play more aggressively through the opening game.
How do you play the Kings Gambit?
I like playing 2... Bc5. Many White players, uncertain about this position, often naively play the obvious 3.fxe5? Which falls to 3...Qh5!
The Falkbeer Counter-Gambit, 2...d5, will also rain on their parade(or at least gather ominous storm clouds).
You find it hard to become aggressive with the King's Gambit? Hm...maybe you should be playing another opening. 
Andy, he's asking about BLACK's moves. Of course he finds it hard to be aggresive, White's doing all the "aggressiving".
After 2... exf4 white does not have to play 3 Nf3 . 3 Bc4 is also quite acceptable .
3.Bc4 is rather an inaccuracy. After 3...d5! white has an unpleasant choice between surrendering the bishop pair for no gain (4.Bxd5 Nf6 5.Nc3 Nxd5!) and risking being positionally strangled: 4.ed5 Qh4+! 5.Kf1 Bd6 6.Nf3 Qh5 7.Nc3 0-0, when white's position is simply bad (although Topalov managed to blunder in a winning position and eventually lose against Judit).
3.Nf3 is the best move, when 3...g5, 3...d5, 3...d6, 3...Be7 and 3...Ne7 are all good, resulting to balanced positions with best play from both playwers.
pfren, the Bishop's Gambit was played by Fischer(and, according to your own post, by Judit Polgar). So if these two top-class players play it, how can it be an inaccuracy?
Of course, Nakamura played 1.e4 e5 2.Qh5?! at a grandmaster's tournament, so I suppose anything is possible.
There are also other strong players which tried the Bishop's gambit, but this does not change much: 3.Nf3 is surely enough more sound.
For the record, Judit did win that game against Topa, but she did not repeat the experiment since.
After 2... exf4 white does not have to play 3 Nf3 . 3 Bc4 is also quite acceptable .
3.Bc4 is rather an inaccuracy. After 3...d5! white has an unpleasant choice between surrendering the bishop pair for no gain (4.Bxd5 Nf6 5.Nc3 Nxd5!) and risking being positionally strangled: 4.ed5 Qh4+! 5.Kf1 Bd6 6.Nf3 Qh5 7.Nc3 0-0, when white's position is simply bad (although Topalov managed to blunder in a winning position and eventually lose against Judit).
3.Nf3 is the best move, when 3...g5, 3...d5, 3...d6, 3...Be7 and 3...Ne7 are all good, resulting to balanced positions with best play from both playwers.
But the bishop doesn't have to sit there, does it? Forgive me if I'm missing something but the following position looks fairly appealing to me. :)
1.e4 e5, 2.f4 exf4, 3.Bc4 d5, 4.Bxd5 Nf6 5.Bc4 (Nxe4, 6.d3 N... 7.Bxf4)
NB! Please note, I don't mind the king coming to f1 on an eventual Q-check - think Qh4 is a sitting duck, actually. :)
But the bishop doesn't have to sit there, does it? Forgive me if I'm missing something but the following position looks fairly appealing to me. :)
1.e4 e5, 2.f4 exf4, 3.Bc4 d5, 4.Bxd5 Nf6 5.Bc4 (Nxe4, 6.d3 N... 7.Bxf4)
NB! Please note, I don't mind the king coming to f1 on an eventual Q-check - think Qh4 is a sitting duck, actually. :)
You should probably mind being immediately slaughtered after 5.Bc4?! Nxe4 (5...Nc6 is also good) 6.d3?? Qh4+ though... 
Like I said, I don't mind coming to f1 with the fat man - if I'm not mistaken, it's a book move.
In any case, you'll get free development immediately after by Nf3. If the Knight has stayed put, it'll get somewhat hot for black w. the double threat, right?
Hate to argue, but if you'd be so kind as to enlighten me here, I'd be most grateful. I play the KG any chance I get, you see. :)
By the way, I'm not arguing whether 3.Nf3 is sounder than 3.Bc4 - that's a given, I think :)
Like I said, I don't mind coming to f1 with the fat man - if I'm not mistaken, it's a book move.
In any case, you'll get free development immediately after by Nf3. If the Knight has stayed put, it'll get somewhat hot for black w. the double threat, right?
Hate to argue, but if you'd be so kind as to enlighten me here, I'd be most grateful. I play the KG any chance I get, you see. :)
By the way, I'm not arguing whether 3.Nf3 is sounder than 3.Bc4 - that's a given, I think :)
Well, if you don't mind about 5.Bc4 Nxe4 6.d3 Qh4+ 7.Kf1 Qf2 checkmate, then I'm afraid I have no good suggestions for you.
pfren, the Bishop's Gambit was played by Fischer(and, according to your own post, by Judit Polgar). So if these two top-class players play it, how can it be an inaccuracy?
Of course, Nakamura played 1.e4 e5 2.Qh5?! at a grandmaster's tournament, so I suppose anything is possible.
Fischer also played 1 b3 once, does that mean it is a viable attempt for opening advantage, or even that he thought it was? Of course not.
This is the logical fallacy of "appeal to authority" - the idea that if someone respected agrees with a proposition, no matter how false or ridiculous, it must be correct.
Yes and even the "appeal to authority" fails because Fischer played the King's gambit in a grand total of.... 5 games in his whole career (I'm not counting simul).
It's probably good against club players that don't know how to handle it, but it surely isn't a top notch opening.
After 2... exf4 white does not have to play 3 Nf3 . 3 Bc4 is also quite acceptable .
3.Bc4 is rather an inaccuracy. After 3...d5! white has an unpleasant choice between surrendering the bishop pair for no gain (4.Bxd5 Nf6 5.Nc3 Nxd5!) and risking being positionally strangled: 4.ed5 Qh4+! 5.Kf1 Bd6 6.Nf3 Qh5 7.Nc3 0-0, when white's position is simply bad (although Topalov managed to blunder in a winning position and eventually lose against Judit).
3.Nf3 is the best move, when 3...g5, 3...d5, 3...d6, 3...Be7 and 3...Ne7 are all good, resulting to balanced positions with best play from both playwers.
3 Bc4 may indeed be an inaccuracy but my point is that 3 Nf3 is not the only choice there , even though it may be the best one. Spassky almost always chose 3 Nf3 but he has also played 3 Nc3 . I also think that below master level an " inaccuracy " isnt nearly as critical as it is above the master level .
What kind of variations should I expect from this? I've played this opening before, but I always find it hard to become very aggressive with it. Any suggestions?