You essentially gamble a little bit. Most people get insurance through work (or they are part of a family plan). Generally, you'll have a few plans to choose from. If you are older, or have recurring issues, you might pick a plan that's a little more expensive, but covers more costs. If you are young and healthy, you might pick a cheap plan, essentially betting that you won't really need healthcare other than your yearly checkup and some vaccines.

The biggest thing with healthcare in the US is that it's very complex. Even if you have insurance that should cover something, it can be hard to find a doctor that's part of your insurance, so people often put off going to the doctor, which is part of the reason why costs are high. Teeth and eyes have separate insurance cause they are optional, apparently.

You basically have "premiums" that are your monthly payment. If you get your insurance through work, they cover a percentage of that; generally a pretty hefty amount of it. They usually don't outright tell you what percentage, though, so many people think insurance is cheap, and get a rude awakening when they lose a job, and suddenly can't afford $1000 a month when they used to be paying $100. Those premiums are taken out of your paycheck pre-tax, too, which gives you even more of a benefit if you have a job.

Depending on the "style" of the plans, they cover things differently. They all (I think) cover "preventative care" completely, which includes your yearly checkup, vaccines, and birth control for women. After that, some plans have "co-pays", which are set costs for a few things, like $25 for a normal doctors visit, $50 for a specialist, $100 for an emergency room visit. Some just cover a percentage of those costs, and some don't pay anything until you hit a limit (the deductible). Finally, there's an "out of pocket" limit. That's most you'll have to pay in a year, after which point the insurance covers everything.

All together, I pay less than $1000 a year for healthcare, but if I got really sick, and needed a bunch of expensive healthcare, I would quickly hit my out of pocket maximum, which I think is like $6,000. I could cover that, but many people cannot cover an expense like that on short notice.

The number on bills is very misleading. The hospitals know that insurance will negotiate down, so they start high, and then after the negotiations, insurance will pay some or all of the remainder. If you don't have insurance, you typically don't pay that whole number on the bill, either, cause the hospitals recognize that they dont have to adjust it up for the negotiation. You can still negotiate on your own, though.