Steve - if you're installing on an interior wall, you can push in on the wall board to find structure behind it and screw into that.
If you're hanging a small cabinet, I'd try to find structure in the wall on the left and right ends of the cabinet space and screw a board to the wall and fasten into that structure. Then hang the cabinet onto that board and fasten to it.
Cabinet makers and installer reading this may have better instruction on this. I am barely a DIYer