I never played over many Morphy games, but I probably should have because they are very instructive. His opponents made a lot of typical mistakes that amateurs see in their games today and Morphy showed how to capitalize on them with quick development and his games are lessons in tactics.
Genius that he was, Morphy's play was not error free. Steinitz published a series of articles in 1885 where he pointed out that Morphy was prone to misplay positions where static features predominated and there were no sound tactics available. Where Morphy excelled was in his fantastic ability to see combinations and his calculating ability. He understood the value of the initiative, development and how the pieces interact with each other much like Alekhine was to do after him. As one author put it, Morphy relied on dynamic, if temporary, advantages.
You don't see the Goring Gambit (1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.c3), which is closely related to the Danish Gambit (1.e4 e5 2.d4 exd4 3.c3) much these days, but it was a staple in the 19th-century. When white plays 4.c3 he threatens to play c3xd4 creating a classical P-center with pawns on d4 and e4 which would allow him to control the central squares c5, d5, e5 and f5. The Goring Gambit has never gained much popularity but guys like Jonathan Penrose and Ljubomir Ljubojevic occasionally played it in the past.
If Black accepts the gambit, White will generally put pressure on f7 with Bc4, Qb3 and/or Ng5. After 4...dxc3, White can either recapture with 5.Nxc3 or offer a second pawn with 5.Bc4, which is riskier but also more dangerous.
If Black declines the gambit with 4...d5, then White often gets an isolated d-Pawn, but he has active pieces. Black has other ways of declining the gambit such as 4...Qe7, 4...d3, 4...Nge7 (intending 5...d5) and 4...Nf6 or he can choose to play passively with 4...d6 or 4...g6,but the disadvantage of those moves is that white obtains a strong central P-formation with 5.cxd4.
Morphy's opponent in this game was a friend of the Morphy family and a contemptible fellow who thought slavery was a good thing because it allowed genteel folks like himself the opportunity to pursue more intellectual and important things. As for the slaves themselves, they didn't matter, I guess. I blogged about him HERE.