Where is the transformer and what does it look like and how can I tell if it is bad?

Inside your air handler. It is rectangular, Has 2 wires- 120 volts coming in and 2-4 low voltage wires coming out. To check you need a volt meter. Check line voltage, should have 120 volts coming in and 24 volts on low voltage side. Remember, you are dealing with electricity, so please be careful.

Found you a picture, go to http://tinypic.com/hvx6vm.jpg The thing near the top center with the wires coming out the one side is the transformer. Most of them look similar. This one is from a post by Modern Daze. Used without permission.

Likely yours in in the air handler, follow the wires from the thermostat or outside unit. It should have black and white wires from the house connected to it and a red and a blue wire going to the thermostat and other parts of the system. If the black and white wires have 120 volts, and the red and blue don't have 24 volts, the transformer is bad. Heat pumps may use a different color of wire. The black wire may not connect directly, but go through a fuse on a circuit board.

I am trying to change a thermostat for my heat pump which is old, but was working fine. Can't get heat pump to come on or do anything. Do I have new thermostat wires connected wrong and I should have someone rewire. Is it likely if thermostat is wired wrong, it could have damaged heat pump,like blowing transformer.