Before you begin anything with a three-way, you must understand that in order for you to have a three-way circuit you must have three-way switches. They are not the same as a regular switch at all. And a four-way is very different again. But that’s on a different page.
When most DIYer’s think of installing a 3 way their brain starts to melt. The fact is it’s very easy. You just need to overcome all those extra wires. Look at the diagram below. You’ll notice we now have travelers. These are the extra ones. But wait, your 3-way switch has two extra screws. So basically, you just need to add those wires to those screws and both switches. Yea it’s that simple.
3-way switch install
However on each 3-way switch, you have a black screw, this is the special one. On the power coming in from the panel, you would connect that black wire to the one black screw. And on the other switch, you would connect the black wire coming from the light to that black screw. The black and red wires in that 14/3 wire would connect to the other two screws.
You connect all white wires together in each box. But of course, the light itself will need that white wire (neutral) to power up. All grounds are tied together and connected to each switch in the box it is in.
Very simple, don’t you agree now.
This is very easy and common how to wire a 3-way switch
If you have Lutron dimmer you might want to read this PDF file.