If you have the special gear to do this it's easy, but how can you do it if you DON'T have the special gear?
One way is to simply cut the chip off the board. The gear needed: Soldering iron, liquid rosin flux (the type cut down with alcohol, not the paste type), a SMALL pair of diagonal cutters, a sharp Xacto knife, and either a vacuum desoldering iron or desoldering braid.
If the pins are as big as the ones on an SRAM IC then take a SMALL pair of diagonal cutters and snip each pin INDIVIDUALLY as close to the body of the chip as possible. You don't want to do more than one pin at a time as you'll probably pull a trace or a solder pad off the board which severly complicates the repair.
If they are small pins or if it's a PLCC type mount (where the pins bend down in a J shape under the chip for soldering) then use a VERY sharp Xacto knife to cut the pins where they meet the body of the chip. Small pitch pins can be cut with a single pass where thicker PLCC pins (the J shaped ones) may require a few passes across to cut through. BE SLOW AND DELIBERATE when cutting. Don't put too much pressure on the knife blade. If you do you'll cut through the pin and down into the board - probably cutting traces which complicates the repair.
Take your time and before you know it the chip will be off but the pins will still be there. Here'e the magic of the rosin flux. Brush a light amount on the cut pins, place a small ball of solder on the tip of the soldering iron, then use the ball of solder to simply wipe the pins off the board. DO NOT use much pressure when doing this or you'll wipe the trace and pads off the board too.
Next use the desoldering iron or braid to carefully clean the solder pads on the board. The cleaner the better as that will give a level mounting spot for the new chip. This is critical as the chip will need to be resting on the pad and not on top of a blob of solder for proper and reliable soldering. Don't use too much heat or the pad will lift off the board!
Now lay a thin layer of rosin flux on the pads and lay the new chip down carefully. Make sure it's oriented properly for pin 1 location and for pin alignment on the pads then tack solder down the corner pins. Lay a thin layer of rosin flux over the pins and pads.
To solder, place a small ball of solder on the tip of the iron, hold the board up at an angle then slowly run the ball of solder down the pins/pads to solder it in place. To fix bridged traces simply wipe the tip of the iron clean, dab a little rosin flux on the bridge and touch the iron to where the pad/pin is and the excess solder will wick down to the iron.
The rosin flux is key as it keeps the solder clean and shiny (no cold joints) as well as helping the solder to stick to the pads/pins and not bridge the pins.
It takes practice do to this without damaging the board but it can be done.