Yes, a grain filler can already have your choice of stain in it, if you want.  It is almost like a 1/2 liquid, 1/2 pasty liquid.  I remember using it high school shop.  You apply the product evenly over the entire board.  Let it set a bit, I think.  Then you need a clean cloth and wipe the filler/stain at a 90 degree angle of the grain or across the grain. The first cloth takes off most of the filler.  Then you come back with another clean one and then maybe a 3rd clean cloth.  You need to get out of any corners.  Each time you are wiping across the grain, this lets the filler stay in the grain.  Grainy wood has small pours in it that you are filling.  Harder wood has smaller pours and you usually do not use a filler. 

You tube would surely have something on this.