You've got to look into pocket hole joinery. The idea is simple: a jig and special drill bit allow you to drill an angled hole that both pre-drills the wood pieces and provides a recess for the screw head. Special pan-head screws hold the wood pieces together. This technique can be used to make a wide variety of wood joints -- even face frames.
Kreg is the leading brand and they offer systems from $50 to $140 -- all are highly rated. I bought the $50 version and now wish I had the case that comes with the $75 version. Note: you need screws of the right length to match your project.
The basic setup ($50) : Kreg R2 Rocket Pockethole System
The mid-range set ($75) : Kreg K3SP K3 Pocket Hole Jig Standard Pack
The deluxe set ($140, $120 with rebate) : Kreg K3MS K3 Master Pocket Hole Jig System