The Portuguese Gambit is an aggressive line in the Scandinavian Defense and begins with the moves:
1. e4 d5
2. exd5 Nf6
3. d4 Bg4
The most common reply after d4 is for black to take with the knight Nxd5 but the Portuguese Gambit allows black to continue getting attacking pieces involved in the game while avoiding the material game just yet.
With the queen under attack white can either block the attack or start their own attack with Bb5+.
Black will respond with 4…Bf5. There is no reason to retreat back to d7. Black should stay aggressive and Bf5 keeps more material in the attack. If white plays c4, trying to hold onto the d5 pawn, then black should continue to give up material with 5…e6. While it may feel odd to let white take 6. dxe6 black should also continue with Nc6 and let white continue taking material. After 7. exf7 Kxf7 black has most of the attacking pieces developed. White has none. It should be a very good attacking game for black.
Just take with 4…Qxd5. Taking with the knight on d5 is also fine but getting more material involved is better in this variation. They will usually play Nc3, attacking the queen, and you can play Qf5.
This is the best response from white as it takes awhile many of the aggressive lines that black wants to go down. 4…c6 will stop most of the attack white has but be prepared for lots of exchanging without the big attack black was hoping for. It should still be a very good game for black.
This is a pretty defensive move from white and so being aggressive is the way to go. 4…Qxd5. The key difference is that after they play Nc3 the queen should now come to a5 instead of the previous Qf5.
Below you can watch all of the lines referenced on this page and see a much deeper analysis on the Portuguese Gambit.