You can paint over water damage now, but honestly, it is better to repair that part of your wall and then paint it. Yes, the latter is a longer, more tedious process, but it is one you can be truly proud of if you DIY it. To get you started, here are some basic instructions and tips.
Check for Plumbing and Electrical Wiring Behind This Wall
There is a good chance that this wall has damage because of a leaking pipe or dripping ceiling. You are going to want to check for any plumbing in this wall behind the ugly spot you want to wipe from existence. If there is no plumbing there, check for electrical wiring as well. Since the next step is to cut away the water damage, you want to be absolutely certain that your reciprocating saw does not accidentally cut pipe or electrical cables and wires while you are cutting! If there are no wires, cables, outlets, switches, and pipes anywhere in the area where you are cutting, then you can move on to the next step.
Use a Yardstick to Mark off the Area You Will Cut, and Then Cut
Next, use a yardstick and a pencil to mark off the area of the wall you are going to cut away. Make sure the lines are even and straight. Then use a reciprocating saw to cut away the area of wall you have marked. Give this area a good rapping with a rubber mallet or hammer to break it up and knock the cut piece loose. Pull it all out and throw it in a bag.
Check the interior of the wall and the exposed wood. Treat it for mold/mildew if they are present. Then cut a new piece of drywall the same size as the current hole. Use sheetrock tape to secure this new piece of drywall in place. Now you are ready to plaster and paint.
Plastering and Painting
There is spray plaster in a can, which is called "orange peel." It is the most common modern method of applying a texture to a wall. The can will allow you to apply the textured plaster in fine, medium, and large grain to match the texture currently on your walls. If your home is much older with a very different sort of plaster texture, you might want to call in a residential painting contractor that does construction painting and plastering. He/she can best match the texture of the surrounding plaster so that the wall looks completely restored. Then either you or the contractor can finish the job by giving the room an entirely new coat of paint.