wiring switch off a 14/3 receptacle
Get a meter.  Set it to measure Volts, AC, in the 250 v range.

Stick one probe into the short side of the upper outlet, and the other in the short side of the lower outlet.  

If it reads ~240 volts, then this is a split outlet, that is both outlets are on separate breakers, and the neutral is shared.  This is old code, and was done so you can plug in both a kettle and a toaster at the same time without blowing the breaker.

Current code requires a 20 amp circuit, GFCI protected.  This will require pulling new wire (12 gauge). 

Using the existing set-up, You would want to run a 14/2, tapping into EITHER the red/white pair, or the black white pair.