How can I prevent a screw from slipping on a slippery veneer surface when I try to screw it in?
You're looking for a bradawl:



Its business end is like a straight slot screwdriver, only typically smaller and sharper.  You push it into the wood where you want the screw to go, then twist to open a small hole.  The screw tip will then fit into the hole without slipping.  Be careful not to let the tip  of the awl slip as you're pushing it into the surface, especially as you said it's slippery.

You might also get away with using a scratch awl, which has a pointed end instead, so it will make a smaller hole.  If the hole is too small, you still risk having the screw slip out of it.