how do i de-solder multiple points at once from a circuit board?

If you are doing a job like desoldering a multi- pin IC from a board, the simplest way is to cut the pins above the board, and remove the body. Then you only need desolder and remove 1 pin at a time.

Resoldering can be done by hand.

There are special de-soldering iron tips designed for certain types of parts. Tips for surface mount resistors and capacitors look like hot tweezers. Tips for removing up to 20-pin inline surface mount ICs are blocks of aluminum alloy shaped to fit the pin pattern.

For larger ICs with hundreds of pins around the outside, or in arrays of pins underneath, special hot-air guns are used to heat the board up to the point where the solder melts.

If you don't have access to any of the proper tools, then use solder wick (from Radio Shack and other electronic parts stores) and very carefully wick the solder away from each terminal; one at a time, then gently lift the metal lead from the pad, just barely bending it.

For surface mount resistors and caps, you'll need 2 soldering irons.

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You need a special Desoldering Tool that fits your iron. These are supplied in many different shapes and sizes for different chip sizes. These are NOT very good for parts like resistors and capacitors, though.

As for putting them back, unless you have $300,000 for a wave soldering station, you have to solder each pin individually.