Schrader valves have a core inside that unscrews. These valves rarely fail and usually you'd just replace the tube but sometimes this is not so easy eg. on a car, dirtbike etc. Mine was leaky so I swapped it out. There's a special two-pronged tool for this that also doubles as a valve cover. Alas, I don't have one right now. That could be a show stopper but it's not... because this is Instructables.

Here's a video of it with crappy audio: http://youtu.be/72CbxNVqIjk

Step 1: Needful Thingies

Dremel with cut-off disk.
Small ~5mm or ~1/4" flat head screwdriver
Or even better would be a rod of similar size like a framing nail.

Step 2: Carve Out a Slot

Carve out a slot. It should be about 1mm wide, just enough to straddle the central pin.

Depth is about 5mm.

Try it and shave off more metal as you need to.

Remember you might need to shave off some of the sides of the screwdriver not just the slot.

My first try was with a dime, then a quarter. Both were too thin and bent.

Something round that barely fit inside the valve stem would have been ideal.

Step 3: Unscrew

Use your slotted screwdriver to fork in and straddle the flat part of the valve. Look inside the valve and you'll see it just past the pin.

Out with the old, in with the new!

The replacement being one you salvaged from a dead inner tube with this same magical tool.