How do I paint paneling?

Sand down by hand, 2 or 3 coats of primer, paint color of choice, vola!!

Make sure the paneling is clean and dry. Prime with a good stain blocking primer like Kilz. Then paint like painting regular walls. Acrilyc latex paint will work. If the paneling has grooves you can fill them with non shrink drywall patching compound. Just put on enough to fill the grooves. Let it dry overnight. Next day use a damp sponge to smooth the patch. Then prime and paint. Sanding is not good. Not all paneling is wood.

Sure. Use a primer like Kilz and then paint with whatever you want. The primer will keep panel color from showing through the paint, plus it gives a good surface to adhere the paint.

I would use some BIN Shellac Based Primer for adhesion and for stain blocking. Then you'll be good to paint!

Clean and prime - best to apply two coats of a Stain Blocking primer and then paint whatever color you would like!