1) d4 d5 2) Nc3

In your opinion, what should black do next?

Black has a wide range of options. If you play the french or the caro against 1.e4 you might want to propose a trasposition with 2...e6 or 2...c6 since white hardly has something better than 3.e4. The most principled move is 2...Nf6, where white will likely go 3.Bg5 (Richter-Veresov attack). In theory this is not dangerous at all (it's hard to pick up a third black move which doesn't equalize) but white has  practical attacking chances in some lines. 3...Nd7 is maybe the main line, where white might go:

4.Qd3 intending to prepare a quick e4 and O-O-O in most lines. you can meet this with a plan involving e6 and c5 (which makes O-O-O rather dangerous for white) or c6+e5.

4.d3 is usually an attempt to set up a stonewall(d4-e3-f4) with the bishop already developed outside the pawn chain (g5, instead in the stonewall it's normally boxed in at c1). Probably normal development and striking with c5 should mantain things balanced.

4.Qf3 is similar to Qd3, while 4.f3 is an ambitious try (aiming at conquering the centre with a later e4) which doesn't work out particularly well after something like 4...c6 5.e4 dxe4 6.fxe4 e5! 7.dxe5 Qa5 and black has managed to crack white's centre.

In general it's a rather practical line, it's not like you need any theory, just play natural developing moves and act quite vigorously in the centre with e5 or c5 early in the game since which attack might become dangerous if you just sit and wait. 

I forgot that white might want to play a blackmar-diemer with 3.e4!?.

You can allow the trasposition if you want with 3...dxe4 4.f3, but probably black can do even better with 3...Nxe4! 4.Nxe4 dxe4 (i forgot the name, Hubsh gambit maybe?) where white is supposed to have less compensation than in the BDG. for example 5.f3?(a surprised BDG player might decide for this move trying to play his usual setup) e5! leaves white praying for a draw, he is really just a pawn down.

I have played the veresov a bit myself(with nice results), i didn't mean it's rubbish.

Most of my wins came from my opponents playing solidly and just developing while white was building a vitriolic attack, but i often experienced trouble against active play by black, expecially quick e5 plans. I suppose it's foundamentally a balanced game of chess with white being a bit more comfortable.

Yep, Nbd7 is the main line after Bg5, but I've also seen the following recommendation:

3...Nbd7 is the main response, followed by either c6 or c5. But 2...e6 seems to leave little better than playing a French with 3.e4

I've played against this line before.

1. d4 d5 2.Nc3 Nf6 3.Bg5 h6 4.Bh4 e6 and the position bears certain similarities to the Steinitz Deferred, which is my personal preference against the Ruy Lopez. 

If you want to know, in that game White seemed stumped(always prepare your openings properly!) and played e4. I eventually won when he wasted a couple of tempos. Or rather, I gained a couple of tempos by attacking a poorly-placed knight.

An exciting maneuvering tango followed, after which he managed to exchange his bad knight for a decent bishop, but then I managed to gain a neat Pawn Cascade(that is, move the pawn on the file next to the tip of a pawn chain) against his kingside and won a couple of pawns. He resigned eventually.

Thanks everyone! I had the same question!

I know that!