My story

When we came back from our ski trip, our heater broke! I have to get it fixed!!

First of all, our HVAC is Trane XR80, I found  the simple manual of my xr80.

I found a few good videos instruction, they are all good suggestions. And, my friends told me some other tricks also.

Here is a good step by step instruction
Fix the flame sensor
A furnace not blowing hot air
Here are the possible false code
The thermostat shall get correct voltage, which is around 24 - 27 volt.

I went a long way and found out the possible correct procedures.

	
We need to check whether the electricity comes through well into the thermostat. Following this video to make sure correct voltage is read.
	
Next, go the furnace. Before opening it up, there could be error indicators codes. It is very helpful to diagnose.
	
Mine was "normal, no heat calling". I checked those low voltage measure, I got the same reading as those from the thermostat.
	
I should have known that it was the thermostat's problem, as NO signal is sent to the board. 
	
If correct, those reading should be "zero" volt. I missed it badly.
	
Of course, if I passed this step, I need to check the ignition, flame sensor etc.
	
This should be the next episode in case I encounter any error in the future. Fingers crossed.

In my case, I am lucky (and unlucky) that it was a bad thermostat. Simply replacing the thermostat solves the problem.

One more note is that the thermostat serves both “gas furnace” and “heat pump”. One needs to be careful when setting it up.

Revisit HVAC thermostat wiring

Today, one of my friends has a failed thermostat and I am pulling my old note and add some new information as well as following

This guy explains the wiring to HVAC very well, I want to give me a thumb up.
And, he drew a very good diagram.
Checking the power to the thermostat.
Another guy makes an interesting little device to show the wiring diagram!
He has an earlier video on this device, which explains the same concept.
It turns out that he has a series of such device, this time it illustrates the "coil" function.
Another post on a dummy digram also illustrates the connection and how they can fail. He lists out relevant books, more videos and tools to test the system and fix the problem.

I am going to stop here, for more details, see the general post on electricity. And, more on the HVAC post.