How should black meet 2.d4 in the Sicilian Defense?

When playing the Sicilian Defence, what should black do when white's second move is: 2.d4

Should black take the white pawn, or should he continue to develop, by say moving pawn to e6?

In classical chess openings, the first thing white tries to do is build a pawn center with pawns on both e4 and d4. So the first goal of 1.e4 is to follow up with 2.d4, and the first goal of 1.d4 is to follow up with 2.e4. Of course, there is an opponent, so usually white has to shift plans quite quickly, but that's the classical theory.

Black can react in several different ways. If he attacks pawn e4 right now, then white can't really move 2.d4; that's what 1...d5 and 1...Nf6 do. 1...e6 and 1...c6 prepare 2...d5, so that black also gets a foothold in the center. Moves like 1...g6 let white go right ahead and hope that black will be able to sabotage white's center later and use the empty space left behind. 1...e5 puts black's own pawn in the center, makes 2.d4 exd4 possible and opens up lines for the bishop and queen: the classical best move.

1...c5 does slightly less than 1...e5: if white does play d4, black can chop off the pawn, and it opens up a diagonal for the queen, but no minor pieces are freed. The point is that that e-pawn is a center pawn, and therefore more valuable than the c-pawn: if black can trade c for d, he'll have one more pawn in the center. It's a very long term idea and he'll suffer first because he is behind in development, but the extra center pawn is helpful in defence and if he survives he'll probably have a better pawn structure.

So the whole idea of the opening is to play 2...cxd4 after 1.e4 c5 2.d4. 2...e6 would be followed by 3.d5, when black can't trade c for d anymore and white gets a slight space advantage.

This also explains the three main ways to play white against the Sicilian: fight it head on by still going for d4 (either 2.d4 or 2.Nf3 3.d4) and try to destroy black using the development advantage, prepare d4 with 2.c3 ("the only move that takes the Sicilian seriously", van der Sterren), or all the other plans that use d3 instead of d4, trying to show that white can do without d4 and that therefore 1...c5 is silly.

This is the Smith-Morra Gambit. Your opponent plans to play c3 to invite dxc for rapid development. The Smith-Morra is extremely dangerous for black. Even if you do not fall for one of the numerous mistakes that results in a quick win for white, white usually has great development and a lot of pressure for a long time. As someone who plays the smith-morra myself, I would strongly discourage you from accepting the gambit.

There are several ways of declining the Smith-Morra gambit.

d5 (which can lead to a Caro-Kann type position if they play e5, but with the ability to develop the knight to c6)

[FEN ""]
1.e4 c5 2.d4 cxd4 3.c3 d5

d3 (leading to a Maroczy Bind type position)

[FEN ""]
1.e4 c5 2.d4 cxd4 3.c3 d3 4. c4

Nf6

[FEN ""]
1.e4 c5 2.d4 cxd4 3.c3 Nf6

I would recommend declining the Smith-Morra with d5 as the easiest/best way to handle the Smith-Morra.

[FEN ""]
1.e4 c5 2.d4 cxd4 3.c3 d5

Well, Morra gambit is not very dangerous for black. In young age I usually have taken the pawn and played scheme with Nc6, Ne7, pawns a6, b5, e6, f6. Later I have become a huge fan of hedgehog systems, that's why I give pawn back after 3... d3. The problem with this hedgehog is that White have some extra tempos there and they can use them if they go to Bishop b2 fianchetto. It is dangerous to play this position by Black, if White player has good openening knowledge but Black didn't.

You mean in 1e4 c5 2d4 right ?

Well the point of the sicilian is to trade our c5 pawn for d4 and open the c file and get rid of white's center pawn

Anyway, that line u talk about is called smith-morra gambit

See this video for better preparation here