Say they made you a member of the Academy tomorrow. How would you judge? What would be your criteria? How would you vote, and why? Answer those questions and you’ve answered your own question about the “judging process.”
Each individual chooses for themselves what’s important. They may know more about film than you or I, but it still comes down to personal choice. Other than choosing what’s eligible, there are no rules they have to follow, at least, in the final balloting phase.
During the nomination phase, branch nominates branch. Only AMPAS member actors can nominate the acting categories. Only Art Directors can nominate for Art Direction. Only Directors can nominate directors. Only Sound Editors can nominate in the sound editing category. Only Costume Designers can nominate costume designers. And so on. Everyone can nominate Best Picture. Only special juries, as noted, can nominate Foreign Language, Documentaries and shorts.
Ever hear the adage “It’s an honor just to be nominated”? It’s unfortunately become somewhat of a scornful cliche, accompanied by an eyeroll and “yeah, sure, right” tone of voice. That’s so undeserved. Of course nominated people would actually want to win and might be disappointed if they don’t, but because your nomination is chosen by your direct peers (actors, sound mixers, cinematographers, etc.) it REALLY IS an honor to be nominated. Seriously, absolutely, no kidding and no eyerolls needed. Ask any nominated person who didn’t win if they would rather be nominated and not win, or not be nominated at all. NO ONE is going to say not be nominated at all. That phrase is only ever said in a scornful manner by people who’ve never ever been nominated for an Academy Award.
Anyway,
Once the nominations are out, then everybody votes for everything, except the previously-mentioned special categories (foreign/docs/shorts).
Do you know anything about Sound mixing? No? Then who would you vote for and why? Answer that and you’ve answered your own question about the “judging process.” Because you’re in the same boat as 98% of the other Academy voters.
Yes, this does point out that people often vote for their friends, and/or things they just like regardless of actual merit (though if it was nominated, merit was there). That’s what they do.
Whatever your criteria is for how they should vote would only apply to you in how* you* would vote, if you were one of them. Each 5000+ voting member of the Academy has their own ideas and ways and reasons for voting the way they do. Tally the votes, and somehow, you come out with a winner, revealed on Oscar night.