Advertisers can only purchase ads to run on certain sites. This page (also here) lists all the sites included:
(In addition to this, there are several other sites currently testing advertising that are running ads for Stack Overflow for Teams. It is not yet possible to buy ads for these particular sites.)
Ads only run on the main pages, not metas. Advertisements are either for the "top leaderboard", "sidebar", or "mid-page leaderboard".
This means that Stack Overflow (the company that owns the network) is making money off ads on other sites, but not this one. However, visitors to this site may visit other sites that have advertisements via e.g. the Hot Network Questions sidebar.
Note that Community Promo Ads are different. All sites have Community Promo Ads (if there are ads with enough upvotes to be shown), but it doesn't generate any revenue. Neither do house ads, which are ads that advertise questions on other sites.
Amazon Affiliate Links
You may not have noticed, but there is one subtle way this site makes some money: Amazon links. Whenever someone links to Amazon.com, the link becomes a Rads.stackoverflow.com link, which means that if someone clicks and buys a product they know that Stack Exchange referred the person and pay them a small portion of the profit from the sale. Across the network this “paid for far more than [some employee’s salary] each month”.
According to the post where it was first announced:
A sponsorship generally entails enabling ads relevant to the subject and affixing a small "sponsored by..." logo in the upper-right corner.
Currently, there are two sponsored sites:
It's important to note that these sites are (currently) beta sites in almost every respect (for example privilege levels), but they have a design.
Stack Overflow is the biggest site in the network and generates the most revenue. The following are Stack Overflow-specific revenue generators:
Yes, there are 250+ people employed by Stack Overflow. Management is listed here. The Community Managers are listed here.
I'm not sure what happened to the list of all employees, but you can find an archived list here.