If you need to paint over existing paint, you may be disappointed if you don't do it properly. Even as you are applying the paint it may look okay, but show through later. There are a few things you can do to minimize this.
Prime the Walls
Before you attempt to paint over a wall that already has paint, you need to prime the wall. The primer will create a barrier between the new coat of paint and the old color. It also creates a more porous surface so the new paint will have a more finished look. Many paint manufacturers are making paint with built-in primer. These are good for paint on a new wall, or unfinished wood, but a wall with color should be primed with a separate primer first.
To prime the walls, you should use a thick roller brush and paint an even layer all across the wall. Don't skimp on the primer. This won't be seen later, so you can afford to paint it on thick. A primer will be applied in the same manner as paint.
Wait for the primer to dry. If you can see the original paint color through the primer, you want to use a second coat of primer. This isn't uncommon when you are trying to paint over walls that have a dark color.
Paint the Wall
Once the primer has been given adequate time to dry, you can start painting. You want to use a roller brush for this as well. One of the mistakes many people make is to apply the paint too thinly by over rolling. You want an even layer, but you still want to use plenty of paint. Using too little will result in the original color showing through, even with the primer in place. This is why it's important to use a good quality paint. Cheap paint tends to be thinner, and won't give you good coverage.
Add a Second Coat
Allow the first coat of paint to dry completely. This will allow you to see just how much coverage you got on the first go. Don't assume you can just touch up a few areas. To get the best-finished look, you will want to apply a second coat to the entire wall, even if you only think it's necessary for a few spots. When you get to those spots, make sure you are using a heavy layer of paint and getting good coverage.
Primer can also be used to cover remnants of old wallpaper. There are several types of priming products available. Be sure you take your time and compare the types available before you purchase one.
Purchase enough primer and paint to leave extra. It's better to have too much than not enough. Since paint is mixed at the source, it can be difficult to get an exact match if you didn't purchase enough the first time around.