The Scotch Gambit arises after the moves 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 (or perhaps 2.d4 exd4 3.Nf3 Nc6) and then, instead of playing 4.c3 giving us the Göring Gambit, White plays 4.Bc4.
At my slowly-expanding Gambiteers' Guild openings site, I have uploaded a series of games and analysis, in the same format as my most up-to-date coverage of Göring Gambit and King's Gambit lines, covering the Scotch Gambit. I have focused particularly on the continuations 4...Bc5 5.c3 Nf6 (which transposes to the Giuoco Piano) and 4...Nf6 (which transposes to the Two Knights Defence with 4.d4 exd4). Both of these lines are commonly recommended to young and improving players, and offer reasonable practical chances at the club level too.
I have also provided quite an extensive list of internet articles for further reading.
A quick summary of the key points:
1. Alternatives to 4...Bc5 and 4...Nf6 are not too challenging, though it is worth knowing about 4...d6 and 4...Be7 (both of which aim to steer play into a Hungarian Defence- in both cases 5.c3 is playable but 5.Nxd4 is objectively best) and 4...g6, against which I don't think White gets any advantage with 5.Nxd4, and should therefore prefer 5.c3.
2. After 4...Bc5 neither side has a good alternative to accepting the transposition to the Giuoco Piano with 5.c3 Nf6.
3. After 4...Bc5 5.c3 Nf6, 6.e5 and 6.0-0 are both fully playable and suffice for dynamic equality. 6.0-0 is a gambit continuation while 6.e5 tends to be more positional.
4. After 4...Bc5 5.c3 Nf6 6.cxd4 Bb4+, 7.Nbd2!? is an interesting sideline which can lead to unbalanced and equal play, 7.Bd2 is safe but can lead to level situations, and 7.Nc3 is tricky but probably not fully sound.
5. After 4...Nf6 5.e5, the Modern Two Knights, 5...d5 6.Bb5 Ne4 7.Nxd4 leads to relatively positional channels, but White can usually get some long-term attacking chances on the kingside. 5...Ne4 tends to lead to open and tactical play with chances for both sides, and White has three good responses, but 5...Ng4 (recently recommended by James Schuyler in his book The Dark Knight System) is currently proving problematic, with Black having a choice of promising continuations.
6. After 4...Nf6 5.0-0, White gets good chances in the Max Lange Attack with 5...Bc5 6.e5 d5 7.exf6 dxc4 8.fxg7! Rg8 9.Re1+ followed by 10.Bg5.
7. After 4...Nf6 5.0-0 Nxe4 6.Re1 d5, the Canal Variation 7.Nc3 appears dubious but 7.Bxd5 Qxd5 8.Nc3 leads to equal chances after 8...Qa5 or 8...Qh5. Stefan Bücker has introduced an interesting pawn sacrifice idea that works in both variations (9.Nxe4 Be6 10.Neg5 0-0-0 11.Nxe6 fxe6 12.Bg5!?, with the idea 12...Re8 13.Re4) but it seems that even the traditional lines (8...Qh5 9.Nxe4 Be6 10.Bg5 for instance) offer both sides reasonable scope to play for a win below grandmaster level.
I've also tried to look at these lines from both sides' point of view- particularly the Two Knights lines as I also have a fair amount of experience from the black side of those.