My 2008 Envoy Denali's heater blower is intermittent. Sometimes it works and sometimes it doesn't. Usually if it does not work when I start the vehicle, I can restart the car a couple of times and the blower will then come on. If I turn the car off while the blower is working, it continues to run. Once the blower is on, if I try to change the blower speed, it may shut the unit off. again, sometimes does, and sometimes doesn't. I am mechanically inclined and would like to fix myself if possible..

We have blower motor resistor problems with our platforms. Take the plastic kick panel off below glove box. You can look up and see the large 5" resistor board with 2 small screws that are offset. Remove the resistor's screws, check the connector for melting, again, pretty common. Drop the glovebox door all the way down, release the spring on left hand side. If I were you, I'd buy a brand new pig tail and resistor. Both tend to melt on us.

Since you are mechanically inclined, now is the opportunity for your electrical skills.
Disconnect the plug from the back of the dashboard switch, and using a VOM (Volt-Ohm-Meter) check the plug for current when you turn on the ignition key.
The hot lead should immediately work.
If the electric meter shows the same intermittent reading you are describing, it is time to fine the relay that controls the current to that switch.
It may be under the dash, or more probably under the hood. Perform the same tests with the plug to that relay.
You should find the problem either with the switch or the relay.
Oh, yes, one more thing.
I had these same problems and found rusted/corroded wires inside the plugs, look for those with a magnifying glass.
God bless your efforts,.