What is the best way to paint brown wood paneling?

First apply a good, even coat of primer (kilz interior primer/sealer works well on paneling)
Once the primer has dried completely you will be able to see clearly where any holes or cracks are in the paneling, as you will want to fill any such voids before you apply the paint.
When the primer is dry and all the nail, tack and screw holes are filled you can then apply the paint.
I like to use a short nap fleece roller cover for surfaces like paneling. The fleece (sheep skin) rollers are a little more expensive but they do not spatter paint everywhere like other roller covers and they last a lot longer.