Wood decks can be painted instead of stained. However most people use semi-transparent or transparent stain because they prefer the natural look of wood. If you choose to paint your deck make sure you select a paint specifically manufactured for exterior wood decks. Most paints won't hold up well with all the foot traffic and weather damage wood decks need to endure. When selecting a color consider how difficult it will be to keep clean. White painted decks are always going to look dirty.
Before painting you should remove any furniture or grills, clean the deck, and cover up any surfaces with tarps that you don't want splattered with paint. This includes the house siding, windows, and doors. Check the forecast and avoid painting when rain is on the way. When you are ready apply two coats of exterior primer. Use a roller or brush to evenly apply the primer. Make sure each coat is completely dry before proceeding. Try to evenly apply the paint to prevent pooling. You may need to apply more than one coat of paint. Afterwards you will probably need to touch up railings with a finer detailed brush.