Gerbils are probably the most naturally tame and easy to handle of all the small furry pets. They are inquisitive too, and actively enjoy the human contact. This makes it possible to handle a gerbil within just a day or two of bringing it home.
To pick up a gerbil, let it come to you. Offer your open hand, and soon enough the gerbil will approach, sniff, and hop aboard. Don't try to grab it from above - anything that approaches from above is viewed as a predator. Eventually your gerbils will become so tame that they will hop onto your hand as soon as you offer it. You can speed up the process by tempting them with some sunflower seeds.
Gerbils are quite easy to hand-tame
How NOT to pick up a gerbil
In the wild, birds are gerbils' natural predators, and they attack from above. So, gerbils are very wary of a hand coming down from above like a hawk to grab them.
Don't lift a gerbil by its tail. The tail may look sturdy, but they are actually quite fragile and can easily be damaged if grabbed. Mishandling can cause the tip of the tail to break off (or an even larger section of the tail). This has evolved as a defence mechanism, allowing the gerbil to escape a predator foolish enough to grab it by the tail. The broken section of tail cannot re-grow, though, but in most cases it will heal by itself. However if you are in any doubt about a tail injury, consult a vet, who will be able to prescribe antibiotics if necessary.
If you need to lift a gerbil to examine it, put both your hands under the body and lift the animal while holding the base of the tail between two of your fingers to stop the gerbil wriggling free.