2.exd5 is the only good move. Then it depends on what Black does.
Against 2...Nf6, don't try to hold on to the pawn. 3.d4!, and then after 3...Nxd5, you play 4.c4! and control the center. After 3...Bg4, known as the Portuguese Variation, do not play 4.f3. You are walking right into what Black is looking for. A quick kill! Play something safe and sound like 4.Be2 or 4.Nf3.
Against 2...Qxd5, the main line with 3.Nc3 is fine, but I prefer the positional line with 3.Nf3!
There is a book out there called Beating Unusual Chess Defenses 1.e4 that recommends this line. It covers the Scandinavian, Alekhine, Pirc, Modern, and Nimzovich's Defense. I believe it covers other responses to a minor extent, but these are the main ones he covers heavily.
I was wondering about the best way to play against the Scandinavian defense. any suggestions?