What happens when you get sick in a country with universal healthcare? What's the process like?

It would be different depending on county and of course how sick you are. There are also many variations. You may for instance choose to use the app, phone in or go there in person. In Sweden the cost may have some variations as it’s set by the country.

If it’s something really serious, like broken bone, massive bleeding, chest pain et.c. You would either call an ambulance or go to the hospital by yourself. The cost for a visit is either 375 (local emergency centre) or 400 SEK (hospital). For Stockholm ambulances is free, but other may charge something like 300 SEK. The stay at the hospital costs 130 SEK/day including everything.

If I get just a minor cold I tell my closest boss that I’ll be working from home to avoid infecting others. Hopefully I’ll have my work laptop at home.

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If it’s something that a doctor need to take a look at I would call my doctor’s office and get an appointment. I could also just go down there and wait. The local health centre has a time for drop-in in the morning. I would usually get an appointment the same day. If it’s nothing serious he/she might subscribe some antibiotics or whatever and it ends there. If there’s a need for more tests or a specialist need to have a look he/she will write a referral. The cost for a visit in Stockholm is 275 SEK (about 27 USD) while phone consultation is free.

If it’s a more serious cold, influenza or something then I call in sick. Unless you have a deal to get higher you get 80% of your salary.