What do you mean by cheap.paint? Are they peeling?. What is the paint, latex or oil? What look are you going after? Fresh paint, country distressed, shinny?
The best thing to do is to clean with TSP. Sand off sheen and prime with Oil based primer and paint with oil based paint. Very durable and cleans easily. Do in semi gloss.
If your paint is flaking, you will need to sand the old paint off. If the paint is securely sticking, you can just prime and repaint.
Peggy....Clean good, sand where needed...prime then paint