Good grip strength improves performance in rock climbing and martial arts, as well as numerous other sports where you handle balls. Grip strength refers to your ability to grab something and pull it toward you or pull yourself up to it. It involves the flexibility and muscle strength of your fingers, thumbs, and wrists. Many exercises don't require any special equipment to make your hands more agile at lifting and holding a lot of weight, and can be improvised at home.
Sports enthusiasts break strength of grip into three types that are best addressed separately, although there will be some overlap. Pinch grip strength measures how well you can hold things between your thumb and fingers. Improved pinch strength will let you grip tiny outcroppings on a rock face as well as grapple with your opponent in martial arts.
Improve pinch strength by purchasing some inexpensive handballs of a medium size. Deflate these balls and fill them halfway with water to add weight. Leaving them only partially inflated, pinch one soft ball with each hand. Try to lift and hold them for 10-60 seconds, depending on your ability. When you get better, hold them longer and walk around. Inflate them with more air or water so it's harder to keep hold, and you're sure to see improvement.
The second kind of grip strength is crushing. Crushing is similar to pinching, but here you try to grab something by pressing it between your fingers and palm, only minimally involving your thumb. This is sometimes called a vice grip. Take small weights off a dumbbell, preferably ones without a lip, and stand them on end so they're parallel to your front. Now try lifting them so your wrists face out and the disc is gripped between your four fingers and flat palm. To make the exercise more difficult, use thicker discs before you increase the actual weight. Books work, too.
Finally, there is holding, or supporting, grip strength. This tests your ability to hold up greater amounts of weight once you have a solid hold, allowing you to pull yourself up a mountainside. The most popular exercise is "farmer's walk." Pretend you must carry full buckets of fresh milk from the barn to the kitchen. If the handles are comfortable enough, buy ordinary paint buckets and fill them with rocks. Carry them back and forth across a room for as long as you can manage.
For more advanced trainers, you can easily build a "grip trainer" from a few screws, an eye bolt, and and a few scraps of wood. Offset the pieces of wood at least the width of your hand, keeping the flat sides together. When you screw them to each other, you have formed a miniature ledge that's 3/4" (2 cm) wide. An eyebolt and chain allows you to attach some weights, so now you are lifting them only with your fingertips over the narrow lip. It can be secured to free weights or a weight machine.
Some exercises improve all these types of grip strength at once. Fingertip push-ups are a challenging but efficient way of building hand and finger muscles. Another idea is wringing out a hand towel. Start with one wet towel in each hand. Roll and compact the towel into a tiny ball in your palm to squeeze out as much water as possible.
An isometric exercise uses your own strength against yourself. Form a fist covered by your other (open) hand. One hand tries to break the grip while the other tries to maintain the compact fist. These kinds of exercises don't exert your body past what it can handle and are less likely to cause pulled muscles or joint damage.