It's typically partly removed from your salary: you join a corporate health-insurance plan, whose premiums are partly but not fully subsidized by the company, with the remaining $x/month after subsidies coming from your paycheck. Some googling suggests that the average employee's share of the premium is $1100/yr for single people, and $5300/yr for those with dependent families. The actual numbers vary (quite a bit) by location and company.

It's a little of both. If your employer doesn't cover 100% of the premium then your share is deducted from your pre-tax salary. Healthcare is often one of the factors up for negotiation in salary discussions. It's not a 1-to-1 ratio, but generally if you opt out of an employer's coverage you can try to use that to ask for a higher salary. I've found it's been far more successful the older I get! The reason is employers want young healthy people in their insurance census (young people are cheap to insure and lower the cost for everyone), not middle-aged people with kids.