How exactly do advertisers take fingerprints and translate that to targeted ads for each user?

A combo of your IP, browser fingerprint plus the fact that you logged in somewhere and that links to your actual name etc. Identify you in isolation is not very useful. It's connecting that identity to another place that's valuable.

The browser history is collected across multiple sites to form a profile. If the user ever enters their email address or logs in, their entire history is deanonymized.