I traveled to Azerbaijan for about 3 days in August 2019, our final destination was the capital city of Baku. One of the reasons I was looking for prepaid sim card in Azerbaijan is quite simple - to call a taxi from mobile application.
Unfortunately, or for luck, this time I didn't actually take a sim-card with internet while in Azerbaijan (it was very quite possible to use public and hotel Wi-Fi during our stay in Baku), but I gathered some information, which might help.
There are three major mobile phone operators currently in Azerbaijan: Azercell, Bakcell and Nar . All three networks are widely modern and reliable with shops located in major towns and cities where one can purchase a sim card or get assistance if needed.
Azercell, Bakcell and Azerfon are often recommended to tourists due to the variety of tariffs available and the help available in a variety of languages. Other mobile phone operators include Aztelekom, AzEuroTel, Caspian Telecom and Catel Eurasiacom.
While in the Baku city center I visited Bakcell shop to learn more about my options, and here is what I was told:
At Bakcell you could get the starter SIM-Card with limited internet data for 25 manats (AZN), a passport is required before signing up.
Bakcell offers different internet packages starting 50 kopecks per day, you could learn more here.