Typical Thermostat Wiring
FIRST!  Turn the breaker off to the unit(s).  This will prevent any mishaps while dealing with the wiring.

You'll want to make a 'roadmap' of how the thermostat is wired now.  Write down which color wire goes to which lettered terminal.  Your new thermostat will have the exact same terminals lettered the same way except in a very few cases.

Replace each wire to the exact same terminal on the new thermostat and you should have no problem.  Don't be concerned with either thermostat wires that are not connected now or terminals that are not used on the new or old thermostat.  If they were important, they would already be connected.  Disregard them, they are for other applications.

If you removed the old thermostat first without noting the wiring arrangement, things are a little more complicated but far from a big deal.  If this is the case, you can try using the roadmaps below.

This is typical wiring for most units.  If you have a digital thermostat now, you MUST pay particular attention to any wire placed at the C terminal on the thermostat.  (Typically the blue wire).  If you are reinstalling another digital or programmable thermostat you will reuse this wire.  If not, discard this wire and tape off the end to prevent shorting and stick it back in the hole to hide it. 

This is the common from the transformer and you can damage the transformer if this wire comes in contact with any of the others, particularly the red so handle it carefully if you didn't turn off the breaker to the unit(s).
and put the wires on the same terminals on the new one as the old one and you should be safe.  Some technicians just use whatever wires are available and don't follow a standard color coded wiring method.

All information here should be considered conversation.  If you are not familiar with electricity, (though this is only 24 volts), and are uncomfortable with dealing with electricity it would be wise to hire a qualified technician to complete the task.  We accept no liability what so ever for any event that may occur as the result of anyone using this information.
Heat Pump T-Stat Wiring
ClGas/Electric T-Stat Wiringi
The difference between thermostats is that with Heat Pumps the thermostat calls the indoor blower on where gas furnaces and electric heat strips turn the blower on themselves after a certain period of time.  Typically 30 - 90 seconds.   Older gas furnaces turn the blower on when they reach a certain temperature.

These are common wiring examples.  These are NOT GUARANTEED TO SOLVE YOUR PROBLEM OR NOT CREATE A BIGGER PROBLEM!  If you want TO BE SURE you don't have a problem, call a technician out.  If you feel capable, do it but be prepared to deal with any 'negative' consequences should you short something out.

In most modern units there is a 'control circuit fuse', which is typically a 3 or 5 amp 'car fuse' type fuse either in the wiring itself or in the circuit board, if there is one in your unit.  If you work on the unit while the power is on and suddenly it's not working, odds are you blew the control circuit fuse.  Locate it and replace it, WITH THE POWER OFF!

This information is offered as 'conversation' and not advice.  Scott's A/C & Heating, LLC shall not be held liable for any results from any actions  taken as the result of reading this information.

If you have problems, e-mail me or call the office.  I'm glad to help you out over the phone if you're having trouble getting things going.
R - Red
G - Green
Y - Yellow
W - White
O - Orange
B - Blue