The most exciting part of thermostat installation is standards are so handy that there must be dozens of them.
My advice is take a pix of the wiring before you start. No pondering what connected to what if you get confused later. This is also handy with advanced car work.
In addition to the pix, draw a map of how each wire connects to what old terminal and all that. Not necessarily useful as an end product but it does kind of force the issue of studying the wiring.
Also pull the wire out of the wall a little, and tape a clothes hanger or something like that to the wire. That way it can't fall into the wall, which can be quite a puzzle to solve even with the gear to fix it.
Thermostat wiring is much like the old RS-232 standard in that every pin is supposed to be indestructible and can't be damaged by shorting to any other pin at any time, and of course Chinese value engineering means thats not always the case. Shutting the furnace off would probably be wise, even if in theory its impossible to damage anything by a momentary short ckt.
WRT "or called a professional" note that the profit margin on sales will motivate them to not be interested in installing your thermostat, rather than installing their thermostat, and they might not sell a nest. Also a pro HVAC guy makes money installing major machinery, so unless they're hurting for work, getting a guy out there might not be easy/cheap.
(edited to add I wrote from a EE perspective WRT wiring and protocols and pinouts, and one thing I overlooked is the decorative aspect of if you're changing from a giant rectangular to small round thermostat you'll have some painting, maybe even screw hole filling, maybe even hold patching to do, and frankly I donno if HVAC guys will do that kind of thing. Every job an adventure...)
Edit: I installed it myself and as long as your HVAC system is a) decently installed in the first place and b) not too unconventionally weird, you should be able to install it yourself. It's mostly just matching up the wire colors in the wall to the wire colors in the base.
I'd add a minor suggestion to make a wiring diagram of what was there and then match the letters on the old thermostat to the letters on the new one. I've seen some weird stuff where the old thermostat works perfectly with the white wire connected to the "G" terminal... so I'd strongly encourage replicating that weirdness with the new thermostat and connect it to the "G" on the new terminal much like the old, regardless of its insulation color.
I think it comes from using non-standard wire and/or remodeling. I remember running into this with a house that converted from no AC and a humidifier to no humidifier and AC and the wiring colors didn't match the letters but it worked perfectly in the end. Or maybe this was the place that had independently controllable fan but not enough wires to supply thermostat power so fan control wires were stolen for thermo power and the colors certainly don't match but the letters did match and it worked.
I suppose the "correct" thing to do is open up the furnace and rewire it the right way and wire the thermostat the right way. In my infinite spare time. Also if someone finds thermostat wiring intimidating I'd advise not opening the cover of a modern furnace, looks like a cross between a water cooled PC and a bad star trek episode in there...
Anyway the general point is whatever was connected to "G" on the old thermo had better connect to "G" on the new thermo, and ditto for all the other letters, and don't worry about the wire insulation color. Make a map (schematic) and snap some pix before unscrewing anything.
Good luck to OP, its fun to install and complete projects and have a new techno toy. A neurotransmitter hit like the first time a program passes all the required unit tests, or hitting vers 1.0 or whatever else.