Are PC case fans supposed to blow out or in to the case?

In AND out of the case. The purpose is to generate a “flow of air” or an “air current” as it were. In my case I have, oh, six fans? Two on the front are “intake”, one on the side (over the processor and its own fan), one on top and two in the back provide the “exhale” points.

It depends on your needs as well.
For normal use one fan on the back drawing air out is all that is needed.

VERY IMPORTANT!!!

Please Please make sure the fans are “silent fans”
If they’re regular or noisy fans, you will go CRAZY.

As Lovelocke says you need the flow of air so have in and out. But try to have the intake from where the air is coolest so if you have yours under a desk and against a wall you probably one the intake to be at the front and out to be in the back towards the wall.

Also keep your fans clean but don’t vacuum them as this kills the motor.