This chess opening

How does one go about this position? I'm commonly stuck here, and I'm not sure whether I should move e6 and then bc5, fiancetto, or nf6.

Also, what opening is this called?

For black that is

Thats the Sicilian

Sicilian Defense.

Per 365chess, Black's most popular next move is 4...Nf6 (which forces White to defend his e-pawn with 5. Nc3).

http://www.365chess.com/opening.php?m=8&n=46&ms=e4.c5.Nf3.Nc6.d4.cxd4.Nxd4

Whatever you do as Black, don't capture White's knight at d4 since that will centralize White's queen without a good way to drive it off.

If White captures *your* knight at c6, recapture with your b-pawn, not d-pawn, so that your queen doesn't get slapped with Qxd8+.

Black's idea here is a matter of choice.  The following are the main responses - anything other than these 5 are probably dubious at best:

4...g6 - Known as the "Accelerated Dragon"

4...e5 - Known as the "Kalashnikov" after 5...d6, or the unsound "Lowenthal" after 5...a6

4...Nf6 5.Nc3 e5 - Known as the "Sveshnikov" or "Pelikan"

4...e6 - Known as the "Taimanov" - and NO, this should NOT be followed by 5...Bc5.  Instead, 1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 e6 5.Nc3 (5.Nb5 or 5.c4 are also possible - study both - best White gets is equality IF Black knows what he's doing) Qc7 (5...a6 is the old line, considered inferior because of 6.Nxc6!) 6.Be2 (or 6.Be3, which leads to a more agressive, tactical line) a6 (Necessary!) 7.O-O Nf6 8.Be3 Bb4 9.Na4 and now 9...Nxe4?? is a blunder.  Black has other options, like 9...O-O, 9...Be7, 9...Bd6, etc.

4...d5 - This is a very offbeat line that leads to an extremely positional game, possibly somewhat dull - If you want to play this, get "Dangerous Weapons - The Sicilian", there's a full chapter on this line.  I've played it twice as Black in over the board competition, one win, one draw.