You should never apply new paint to paint that is already peeling. You should first scrape off all the old peeling pain and then think about painting. You can then get the paint and brushes and other requisite material and begin painting. Check out tlc.howstuffworks.com/home/how-to-paint-room.htm for details.
Actually if you get a steamer machine from your local hardware store and then use that to steam the paint away and then scrape it of you'll be better off. Also, after that you should go over it with a damp rag to get any residue off
scrape and/or pressure wash..but..first..figure out what caused the peeling and fix problem..water damage..from a leaky gutter,,roof,,other..even ventilation of house..can cause this..but fix..or it will peel again..