The Ponziani Gambit is a stab in the center with 3.d4. Black will accept with 3...exd4. Now as White you have two ideas. You can invest your energies on restoring material balance by recapturing on d4.
This is simple enough but there is another path you can take. This other path is more in spirit with 3.d4. You will allow Black to hold on to his pawn while you build up a lead in development. This is the gambit line.
Play moves like Nf3, 0-0, Bg5, Re1 and so on while your opponent is shoring up his center. Then you will try to exploit his still central King. Force a material or structural concession if he is to castle. Better still, if you can, rob his castling rights. Even if you have to sacrifice further material to do this it's worth it. Then it's time for a King hunt.