Step 1: Stuff You'll be Using
Either a desoldering iron, a soldering iron and desoldering pump, or a soldering iron with desoldering wick or braid.
Solder (It helps, trust me)
Helping Hands (Optional)
Magnifying glass (Useful if you're desoldering surface mount components)
PCB Board to get components from
Water Bottles (Optional, but you'll need them if you're making the containers)
Step 2: Using a Desoldering Iron or a Soldering Iron and Pump
Once you sucked up enough solder, break the leads away from the hole, then pull the component out. In the pictures, I'm desoldering a tact switch from an old stereo. I was lucky enough to have switches with only two leads.
Step 3: Desoldering with a Soldering Iron and Pliers
Clamp the board in your helping hands, and grab the component you want to take out with your needle nose pliers. Heat one of the leads, and at the same time, tilt the component so you pull the lead out. What you'll get is a lopsided component. The idea is to do this while alternating sides until the component comes out. It's a good idea to use locking pliers.
Thanks to Zaen for this tip. Instead of using pliers, wedge a small screwdriver under the component while heating the leads.