Locate the studs in one of 3 ways
locate electrical receptacle on wall. They are generally fastened to one side or the other of the stud. You can open up receptacle and look inside to see stud.
drill small pilot holes in the wall that will be covered by the new shelf or hanging bracket. You will meet resistance and see wood borings on drill bit.
stud finder (agree these are unreliable - go with options 1 or 2)

I suggest once you locate the studs you install a horizontal hanging bracket (made from 1x3 wood or similar material) that spans 2 studs and is fastened firmly to them using a lag screw. Counter sink the screw head if you want it flush. Then fasten the vertical shelf brackets to this horizontal piece. Run a vertical spacer behind the shelf brackets if you want it flush with horizontal member, just be sure that the vertical brackets are fastened to it horizontal hanging bracket.