Well, you can start training right away without even buying any equipment, by training your pinch grip in the gym.
Keeping your fingers straight, grab a weight plate like you were picking up a plate or tray, but just let it dangle from your hand as you stand up. There are a few ways to go from here.
First -- add more plates. You might start with a 10 lb. plate and add another, however many you can hold. This will change how wide your hand is pinching, let's say opening up the "tiger's mouth," since you're a martial artist. Each change in width not only adds weight, but making your hands wider stimulates growth differently.
Second -- keep it to one plate, but make it a bigger one. Greater weight in the same size hand opening will eventually create greater strength in that size pinch.
Third -- grab any configuration of plates and hold for time.
You can do these lifts and holds in the normal sets/reps manner.
You might also add some other exercises. Rope climbing, or twisting a towel over a pull up bar and twisting it and then climbing it like a rope, is a tremendous grip work-out. Simply hanging from a bar is great for endurance. Try grabbing a plate by the hub -- the raised metal around the hole in the center. Try gripping with only the first two or last two fingers.
That's enough to get you started. Luckily, pinching works to give you a pretty rounded strength. Grippers, for instance, don't really use the thumb much, but pinching gives you a more rounded strength. And it will apply to grippers, or elsewhere.
You might also want to get some thick rubberbands for extensor work. Slip em over your fingers and straighten your fingers. This rounds out your hand strength and growth in a way said to help prevent injury.
Eventually, you'll want to get some grippers. Ideally, you'll want one that's relatively easy, to warm up on and do holds on, one that's a bit too hard for you(your "goal gripper"), and one that's much too hard for you, to do negatives on. Most of the tough quality grippers cost roughly $20 or a bit more. So if you want a serious start in gripping, you can get by only spending $20 if you already know what strength gripper you can close, but even if you do, you'll be better off getting at least one or two more grippers.
Check out the gripper sites for more info. They're quite friendly and there's an awful lot of solid info on them.