Why can I not find a stud, and, if there's plywood behind my drywall, do I need to find a stud?

I bought a stud finder (admittedly a cheap one) to find studs in my wall and floor joists in my ceiling. On the wall the finder is very erratic. I started getting frustrated and just drilled like 20 holes in my wall thinking I'll eventually find one. I haven't. What I have discovered is puzzling me. The drill goes straight through for about a half inch, then there is a little resistance, then it breaks through to air. I did not know what would cause this, so I just figured it was the drywall still. My next plan was to take out the outlets and see if its mounted on a stud. Alas I found wood, but its not a stud. Apparently behind my drywall is a layer of plywood. Should this make it very difficult for a stud finding to find studs, and can I just screw a shelf into the plywood and be fine?