Installing doorbell wiring involves running wiring from the doorbell transformer to the chime unit and then to each doorbell. This usually means one pair of wires to each location.
Obviously, this is a big job in an existing home. It will often mean fishing wires which is not impossible, but difficult.
You might want to consider a wireless doorbell unit at this point. See the article, 'Wireless Doorbell Installation' for more information.
Doorbell wire is usually #20 awg and would be two conductors. You may find it in different colors, sometimes 'red' and 'white', other times different colors where both conductors are the same.
The color of the conductors for a doorbell is usually not important. Either conductor can be hooked to either terminal at each connection point. You will want to check the instructions that came with your kit to make sure you are getting the right wire.
Assuming you have a path to route the wire through an attic or basement, this will not be too difficult. Secure the wire with small cable staples and leave enough extra at each termination.