In theory, there are four different ways a carrier can find itself blacklisted.
a) The airline was found by a member country to be operating in an unsafe manner for any number of reason (aircraft not airworthy, lack of necessary records, not following maintenance procedures, etc...).
b) The civil aviation governing body (local FAA) of a country is found by a member country to be totally useless/incompetent/corrupt/unreliable/etc... in which case all airlines from that country are banned (that would be Congo, Equatorial Guinea, Liberia, Sierra Leone and Swaziland).
c) Same as a) and b) but the finding is made by the European Aviation Safety Agency. In practice, a) and b) would be the two cases you'd expect to be the root cause of a ban.
Once EASA or a member state reports a violation as outlined above to the EU, the EU will hold a hearing within 10 days, where the carrier/country at fault can defend itself if it so chooses. A decision is made at the hearing and effective immediately.
There are a few exceptions to these broad guidelines. If a carrier is banned from operating in EU for any reason, it can get around the ban by using wet-leased aircraft. This is true even if the ban affects all airlines from one country, provided that the wet-leased aircraft's owner and country of registration are not themselves banned. This is how Hewa Bora Airways can still operate in the EU despite the ban imposed on all Congolese carriers.
Recep Tayyip Erdoğan has no clothes.