Villagers who work at the research table will produce tech points. There is a different way for villagers to study medicine.
Villagers typically need to be at least Trainee level before they will perform work (farming, building, researching, etc.) on their own.
Until you have purchased Level 2 of Medicine Technology, villagers can only gain healing skill by healing a sick villager. You can click on the "?" next to "Buy" button for any tech to see information about what that tech does for your village.
If there are no sick villagers and you want to train a healer, you should work toward getting Level 2 of Medicine Technology, which will give the villagers a place to study medicine and increase their healing skill.
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Barbara
Unicorn
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