Well there are a few ways. I have used most of these but not all.
So I have a forearm trainer from black diamond, either squeeze it from open hand to closed to open and so on or just close your hand and hold it. Works well I dont use it too much, only when I dont climb for a few days.
Forearm Trainer - Black Diamond Climbing Gear
Next there are more elaborate ones that have springs for each finger but they do the same thing and are more $.
Gripmaster Hand Strengthener - REI.com
Next there is the Gyro Ball, these are fun. Had one for a long time before I actually climbed and needed it. Just spin it to win it.
Amazon.com: Dynaflex Pro Sports Gyro Wrist Exerciser: Sports & Outdoors
Next there is the tie some rope to a small wood pole 1" - 1.5" diameter (ish) and like a foot long with a weight at the other end of the rope. Stand on a chair and the weight should hang to the ground then just start rolling the pole , this will lift the weight. Have you arms all the way out and go until you get the weight to the top or you can go no more then let it back down slowly.
Next, vertical grip hangs/ pullups. Self explanitory... But here is what I built in my garage.
http://i.imgur.com/RjIKGsN.jpg
Finally there is a hangboard, these are very good but also really hard on your tendons so probably dont do this one right away if at all, just putting it in as an option. These are also expensive but it is what it sounds like. It is a board with different grips that you either hang from or do pullups on. Simple. Personal favorite:
Beastmaker 2000 Series | beastmaker
There are also these, never used them before. They seem to be more for getting "big" I guess and you dont want that for climbing so I have not use them but you might be interested in them.
Amazon.com : Captains of Crush Hand Gripper : Hand Strengtheners : Sports & Outdoors
Hope this helps!