Most thermostats, the front snaps into the back. So the back part is screwed to the wall and you can pry the front off. The screws are probably holding the two parts together.
Once inside you'll see how many wires you have and where they're going. There will be about 12 different slots each labeled by a letter. Mine only has two wires. A "W" wire and an "R" wire.
The C wire provides power, which is necessary for some thermostats. Mine doesn't have it run so I'm on battery.
You'll need to know what method of heat you have. Forced air (high efficiency or not), electric baseboard, hot water radiators, etc...
Once you find the thermostat you want to replace it with you can look up what wires it'll need to function.
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