Pull the chip out evenly to avoid bending pins. The easiest way to do this is with a screw-style chip puller, but a pair of screwdrivers works almost as well (pry alternate ends a little at a time) and can't ruin a socket unless the blades are far, far too thick. Tong-style chip pullers are much worse than either of these tools and should be used only if the chip can't be reached with other tools.
Special tools are best bought from an electronics store, like Radio Shack or Fry's, and not computer stores, which charge too much.
If the BIOS chip is soldered in place, the best way to remove it is with an expensive ($300-$900) desoldering iron equipped with electric vacuum pump. Excluding that, the safest way is to cut the pins off the chip (ruining it), and pull out the remaining stubs while its solder is melted. If you don't want to ruin the chip, it can be removed with .080" or narrower copper desoldering braid and a 30-35 watt iron, but this braid has to be applied to both the top and bottom sides of each pin, and all the pins have to be able to wiggle freely or else the copper traces of the motherboard will tear out when the chip is removed. Always solder a socket in place of the original chip.