Now in the diagram above, The power source is coming in from the left. Notice the black wire is the only wire that we are controlling through the 2-way switch. You have an incoming hot wire (black) going to one screw (it does not matter if you use the brass or silver screw) on the side of the 2-way switch and a black wire from the other screw on the 2-way switch going to the load (light, ceiling fan etc..). The white wires are wire nutted together so they can continue the circuit.
Now as for the ground wire. It is very important to connect the ground wire to the switch as well. The Green screw on the 2-way switch is for the ground so all ground wires should be connected as seen below.
All ground wires (bare copper) are all now connected (incoming ground, load ground and switch ground). This makes for a safe protected circuit by having all grounds intact.
So what have we accomplished. By wiring a 2-way switch, The circuit below shows the basic concept of electricity flow to the load. Let's assume the load you are controlling is a light. The electricity flows from the hot wire (black) through the 2-way switch (shown in off position) and then to the light and returns through the neutral wire (white). This is a completed circuit.
Now by understanding the diagram above, go up to the top diagram and by using the concept shown here, just use your mouse pointer on that diagram and follow the flow from black wire (hot wire) to the load and return through the white wire (neutral). This should give you a good basic understanding how the 2-way switch circuit works and will help you in adding or changing a 2-way switch.
So now that you have a basic concept of wiring a 2-way switch, let's look at the following 2-way switch diagrams to see which type of circuit scenario you have. After you have pulled your switch out from the wall, the wires in the box and connecting to the switch should look like one of the following.
Basic 2-Way Circuit - Power Coming In At Switch
Basic 2-Way Circuit - Power Coming In At Light
Power Coming In At Switch - With 2 Lights In Series
Power Coming In At Light - With 2 2-Way Switches and 2 Lights
Power Coming In At Light - With 2-Way Switch and Outlet
Power Coming In At Switch/Outlet - With Light
Allow Tim Carter from AskTheBuilder.com to show you some great tips for installation and wiring a 2-way switch.