(continued ...) So the wires are all identified and marked. Disconnect them from the old thermostat terminals. Remove the old thermostat. Mount the new thermostat base and land the wires on the appropriate terminals.
Here are a couple of tips. If the new thermostat doesn't completely cover the old thermostat's 'footprint' on the wall, you can get a piece of 20 gauge polished 316L stainless steel cut at our home center just big enough to cover the scar. Sand the edges round with very fine sand paper. Drill a hole for the wires and mount it on the wall first. Another tip is about that hole where the wires come through the wall; sometimes interior wall cavities can be drafty. Use a SMALL amount of expandable foam and squirt it into the wall cavity to seal out drafts from causing false thermostat readings. You want just enough foam that it starts to come out of the wire hole. Let it cure and cut off any excess before completing the installation. Another tip is that if your thermostat is on the outside wall, that is bad and you should move it to an inside wall. If you're contemplating moving it, some best practices in thermostat location are as follows: no outside walls, away from heat generating equipment (televisions, refrigerators, etc.), away from outside doors, out of direct sunlight, near a return air grill entry point on forced air systems and otherwise in a common location served by that system.
Finally, let me dispel a few myths while we're on this topic. One myth is that a set-back/set-up will cause your equipment to run a long time to return to temperature thereby using more energy. The long run time will be true, using more energy ...