Pick a calm, overcast day or work early before surfaces become heated or materials will just evaporate. Never work in direct sunlight.
Mix detergent and water in a bucket and clean the shutters thoroughly using a brush and sponge. Rinse thoroughly and allow to dry before proceeding.
Make any needed repairs to the shutters or the fastening systems holding them in place.
Follow the manufacturer's instructions and use a soft cloth to apply a vinyl cleaner and conditioner. It is best to use one that matches the vinyl sealing product you will use. The cleaner and conditioner will remove the surface oxidation from the vinyl and prepare the surface to receive the sealer. Allow to dry completely.
Apply a vinyl sealer with ultraviolet protection as suggested by the manufacturer. Be sure and put on the number of coats recommended.
Allow to dry, and buff off excess as directed.
Use fine grit sandpaper or steel wool to lightly rough up the surface of the vinyl shutters.
Mask off the windows and walls around the shutters with masking or painters tape and sheets of paper or plastic.
Apply several thin coats of a paint formulated just for vinyl and plastic. This paint is generally sold in spray cans and in a rainbow of colors and does not require a primer. Rust-Oleum and Krylon are two brands with products for plastics and vinyls that should be readily available at paint or home improvement stores.
Alternatively, apply a primer made specifically for plastics. Rust-Oleum offers one in both liquid and spray can form. A super bonding latex primer from any of the major paint manufacturers would be another choice. Any type of finish can be put over these primers.
Brush on two coats of quality exterior latex based trim paint over the primer. Note that paints with vinyl or urethane as part of their chemistry will be better able to adhere to the primer and expand and contract with the changes in temperature of the vinyl shutters.