Holes and tears in a vinyl liner are one of the worst things that can happen to your pool, and depending on how damaged the liner is, it may require a replacement rather than a simple fix. So how do you prevent holes in your liner in the first place?
No Sharp Objects in the Pool
One of the more obvious things is to make sure no rocks, bottles, chairs, or anything that could end up cutting the liner are thrown in. If has sharp edges, or if it doesn't belong in a pool, keep it out.
Watch for Sharp Edges on Your Equipment
Another thing to keep in mind is your maintenance equipment. If the metal on your brush, net, or anything else you use is damaged inspect them thoroughly for metal shards or rough parts. If this has happened to your equipment you can either sand/grind it down or put duct tape on it. It really works and it keeps you from having to buy more equipment.
Also when you brush your pool, make sure that you don't drag or push the brush against the walls of your pool when you are brushing the bottom. Be sure and always leave a brush or net on your pool pole so the pole itself does not damage the liner by mistake.
Be Careful with Pets in the Pool
Some families have pets that like to swim in the pool. If this is your case, you should train your dog to climb out of the pool at your shallow end steps or ladder. However, if a dog panics and can't find the steps, either from being thrown in the pool or gets tired of swimming, they tend to scratch at the wall to climb out.
Ideally, the best way to keep your pet from damaging your pool is to enforce a strict "no pets" policy, including potentially fencing off your pool from the rest of your yard.