The Slav Defense

What is the best response to the Slav Defense for white when c6 is played?

Depends.  What are you trying to accomplish?

it is a very common opening, there are a lot like Nc3, Nf3 , Bf4, even capture on d5 is possible

Best response? 3.Nf3.

Like #2 says, what are you trying to accomplish.  Also, what order Black plays his moves.

1.d4 d5 2.c4 c6 and now.

A) 3.Nc3 - I would only play this move if you intend to meet 3...Nf6 with 4.e3, which leads to a Meran frequently (4...e6 5.Nf3) and makes 4...Bf5 dubious due to a raging attack on d5 and b7.  Otherwise, I do not recommend this move because there are too many other options for Black including 3...dxc4 or the Winawer Countergambit with 3...e5.  It does allow you to play the Marshall Gambit against the Triangle Defense (3...e6 4.e4), but that has a ton of theory.

3.cxd5 - if you like symmetrical positions that are very safe but somewhat drawish, this is your answer followed by Nf3, Nc3, and Bf4.  Note that Bg5 is a mistake unless Black has already played ...e6.  Without ...e6, Black can answer ...Ne4!

3.Nf3 - this is the main line.  Black now has 3...Nf6 or 3...e6.  3...Nf6 can be answered by 4.Nc3 (main line) which allows for the Semi-Slav (4...e6) or main line Slav (4...dxc4 5.a4).  3...e6 is a little different.  4.Nc3 allows the highly theoretical Noteboom with 4...dxc4 and Black will usually keep the pawn with outside passed pawns on the a and b files, but White will dominate the center.  The other option for White in both cases is 4.e3, know as the Slow Slav.  Against 3...Nf6, the main response is 4...Bf5.  Against 3...e6, Black can go into a Meran with 4...Nf6 or a Stonewall Dutch with 4...f5.