The set a base line of “comparable homes” aka “Comps”. The use things like age, number of bathrooms/bedrooms, square footage, and then they look for homes in your are that have recent sold for matches.
They have a history of data that tells things like “a bathroom is work $X” and a “bedroom is worth $Y”, or also things like so much for a detached garage, a new roof, a finished basement. Etc.
So they’ll find 4 or 5 close matches on paper and then made adjustments as I explained above. So you’ll get something like
Nearby Home A matched by square footage, $100,000
You have 1 more bedroom, +20,000 per bedrom
You have 1 fewer bathrooms, -5,000 per bathroom
New Roof = + 4,000
New Heating System = +1,000
Finished Basement = $10,000
So that house, adjusted to match your house, could be worth $130,000
X that by 4 or 5 local houses.
Take the average, and you get your appraised value.
But they include tons of paperwork to back this all, an appraisal might be 40 pages long.
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