It is inevitable that if you are active in the water with your wetsuit at some time you will get a rip or tear in the neoprene. In most cases, there is no need to panic or despair. With a few simple items, repairing a torn or damaged wetsuit is a fairly easy procedure. It may not look as good as new when you are done but the function of the wetsuit will be maintained.
A lot of times when you rub up against rocks or coral or some other rough object the surface of a wetsuit will get roughened up and expose the softer more vulnerable black neoprene below. Short term your wetsuit will work just fine this way but in time the abraded area will grow and it may deteriorate to the point of causing a tear or hole. The best way to repair this kind of damage is to apply neoprene glue to the area. What is called neoprene glue is usually a special contact cement formulation for gluing pieces of neoprene to each other. You can usually get it where you bought your wetsuit and it is usually black or yellow in color. Aquaseal and Black Witch are two popular brands of neoprene wetsuit glue. Lay the damaged area out flat if you can and apply lots of the glue to the area. Spread the glue out with a flat wooden stick, application brush, or other spatula type tool to at least a centimeter or two past the abraded area. Try to spread it out as evenly and smoothly as you can. It is almost impossible to make it look pretty but that is not the goal anyway. You want to reinvigorate the area as best you can and still maintain the flexibility of the wetsuit. Neoprene glue is very smooth and slippery when dry. If the damaged area needs to be used for gripping with most neoprene glues, you can sprinkle a small amount of dry sand over the glue approximately 30 minutes after you apply it. This will give the area some texture for gripping. When you are done let the glue dry at least overnight. Some glues will need longer to dry so follow the directions on the glue containers label.
If the damage to the wetsuit is a simple straight cut or tear with no missing material, you can simply glue it back together using the neoprene glue. Very carefully separate the two edges of the cut and apply glue to each of the sides. Try not to increase the cut when you do this. Then hold the two edges together for a few minutes to let the glue set. With some neoprene glues, you have to let the air air dry for a minute before pushing the two sides back together. As above, let the glue dry at least over night.
If the damage to your wetsuit involves missing material, repairs get more complicated. Most often, the best thing to do is patch the hole like you would a hole in a bicycle tire. Most dive shops have patch material or old neoprene lying around you can buy for patching. Cut a piece of neoprene patch material a few centimeters larger than the hole, apply glue to the top edge of the hole and the underside edge of the patch and apply the patch. Sometimes you will need to fill the hole with material and glue and sew it to the edges of the hole and apply a patch over that but sewing neoprene is often not recommended. The thread usually will not stretch with the neoprene when you dive and over time the thread will cut through the wetsuit.