Most everyone is limited to visiting Europe for a maximum of 90 days out of every 180 days. Over stay that and you risk being banned from entering Europe again.
But long term stay visas are very difficult to get, if you lack immigration privilege.
This list is the most thorough I’ve seen:
Your Guide to (Legally) Staying in Europe for More Than 90 Days (nomadicmatt.com)
Page down to the heading “1. Take advantage of the Bilateral Agreement Hack” to learn about nearly secret agreements the U.S. has with many European countries that may provide a way to stay in Europe, in another country, even if you have reached the 90-day maximum.
Some countries permit stays of up to 1 year after application for a long term stay visa. That too is describe in the above link.
Outside of that, residency remains restricted to mostly skilled, young workers, or via marriage, or via right of descent ancestry privilege, as I have documented previously.