Anchor 1x2 wood on cabinet side wall
Since you are adding exposed supporting bracket for the shelves, and fairly large one at that, 1x2s, screws are the appropriate way to attach and remain removable.  Pre drill the holes and contersink for the screw heads in the wood strips.  Select screw length to just go deep enough in the side without punching through. 

Screws similiar in size to drywall screws- 1-1/4 or 1-1/2" long, Measure the thickness of the wood strip and the cabinet wall to determine the screw lengh. Screws long enough to get good penetration in the cabinet wall without punching through the inside.