
HammerJack |
Pathfinder Roleplaying Game Superscriber; Pathfinder Starfinder Adventure Path, Starfinder Roleplaying Game, Starfinder Society Subscriber

10+proficiency+key stat modifier.
They go to Expert when one of their features says they do. Like this example from Alchemist:
"Alchemical Expertise Level 9
Constant practice has increased the effectiveness of your concoctions. Your proficiency rank for your alchemist class DC increases to expert."

Gisher |
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Here are the proficiency bonuses (next to the last page.)
• Guide to Proficiency Bonuses (web version)
• Guide to Proficiency Bonuses (Google Drive version)
Then, as HammerJack said, just add 10 and the relevant ability modifier.