2020 updates by Cathy Bickel
So you went to the pet store and picked out a cute pair of gerbils from the pet store clerk who handled them so easily. Now you get them home, and rather than happily come out to play, they run away from your hand in the tank. Maybe they even give your hand a nip.
You are going to need to tame your gerbil. Making the transition from "will approach the hand" to "will jump in the hand" can be very, very hard with a gerbil who was not well socialized.
To solve this problem you first must understand a basic fact of gerbil motivation: gerbils are motivated more strongly by time out of their tanks than they are by food rewards. While offering food treats to your gerbil may help boost your gerbil's opinion of you, it is rarely enough to tame a gerbil. You will need to get them out of the tank and having fun for them to become truly tame.
If you are a good gerbil wrangler and can lift a gerbil out quickly and calmly with a two-handed "scoop," use that technique. If you can't, though, don't resort to chasing the gerbil around the tank. This will make your gerbil less, not more, tame. With very shy gerbils it is sometimes actually better to just begin taking them in a way that does not cause them stress, such as by scooping them out using a box or tube.
Gerbils that approach the hand, super-sniff it, then nip it, are the perfect candidate for the fast-forward taming approach. I think they are basically saying, "Gosh, I'd love to trust you that much, but I don't, so please take that thing out of here."
Start by taking your gerbil out as calmly as possible. Sit on the floor right next to the tank. Let her run around on you as much as she does, or doesn't, want. If she tries to leap back into the tank, let her. Then take her out again. Repeat, using as short a cycle as she is comfortable with.
You will almost see the light bulb go on: "Gee, this is fun, and I can go back in the tank whenever I want!" She might jump in, turn around and stand up on her hind legs as if to say, "Again!"
See if you can get her to run down your arm back into the tank, instead of leaping in. Then leave your arm in and see if she'll climb up. This will teach her she can have complete control of her travels by using your arm as a ladder.
Be sensitive to the signals that she wants to go back to her tank. Digging in the palm of your hand is her way of asking for a return. Since it's a relatively polite way to ask, put her back when she does this. A nip is a less polite way of asking. Give her a puff of air on the back of the head and say "No!" sharply. Hold her another several seconds so that you are not rewarding the nip with a return to the tank. Then put her back.
I have seen untamed gerbils learn how to climb the arm tentatively in one extended session of this activity, and with daily repetition, go from untamed to tame, begging to come out, in just a few days. Not all gerbils learn to trust that fast, but gerbils are quick learners. Good luck!