When it comes to refinishing furniture, chalk paint is one of the easiest options, mainly because you can paint right over the existing surface of the furniture without having to sand or prime it.  Not only that but it usually only takes one coat of paint, which means that you don't have to waste a lot of time waiting for paint to dry before you can move on with your project.
The basic process is fairly easy. You simply apply the paint, wait for it to dry, and then seal it with a coat of soft wax. Here are the steps that you will need to take to refinish your dresser:
1. Start by removing any knobs or hardware from the dresser. Wipe the entire surface down with a damp cloth to remove any dust or debris. Allow it to dry thoroughly before moving on.
2. Set the paint can upside down for a few minutes to let any of the pigment that has fallen to the bottom of the can come back up toward the top. When you are ready, flip the can over and stir the paint until the pigment is evenly mixed in.
3. Using a standard paintbrush from your local home improvement store, start painting the dresser. Use even strokes that go with the grain of the wood, making sure that the entire surface is covered. As long as you mix the paint well, you should only need to use one coat.
4. Allow the paint to dry. As it dries, it should take on a beautiful matte finish that looks somewhat chalky. This is how the paint got its name. 
5. Once the paint is dry, you can apply the wax to the surface. Use a clean, soft cloth to buff the wax into the surface using a small, circular motion.
6. If you want your dresser to have a distressed look, you can then take sandpaper and gently sand away parts of the paint to reveal the surface underneath. Typically, distressing looks best if you can place it in the areas where the dresser would normally receive the most wear and tear. For instance, the edges of the piece would probably lose their paint faster than the large, flat areas of the piece.
7. Finish up by applying a coat of dark wax to the piece. Again, use a soft cloth and a gentle circular motion to buff the wax into the surface, making sure to get it into all of the little cracks and crevices.
8. Allow the piece to cure for 24 hours before putting the hardware back on. You may find that the old hardware doesn't look quite right with the new finish. If that is the case, you may want to apply a patina to it to give a more antique look, or you may want to replace it altogether.
Here is a great video that show you the entire process step-by-step: