14/2 wire 2 way switch adding 14/3 wire to make it a 3 way
On the 14/3 cable, tape the white wire with black electrical tape on both ends. This is always-hot.   

Tape the other two wires with yellow tape on both ends. These are travelers.  

The reason to mark with tape is a) with white it's the law; and b) with yellow, it turns a typically very confusing 3-way box into easy mode. 3-ways are notorious for having no color codes at all, and your next 3-way might have white/red travelers.  

In the existing switch box, there should be two wires on the switch.  Whichever one is always-hot is attached to the black-taped white wire from the new /3.  

Next, in each box, the 2 yellow-taped wires are put on the 2 brass (yellow-ish)  screws on the 3-way switch.

In each box, there should be 1 wire left.  That goes on the black screw of the 3-way.