There is a very convenient way of getting around in Baku by taxi using mobile application Bolt (formerly known as Taxify). The best, if you have already installed Bolt for some other city, it will work internationally. 

How to Get around in Tbilisi by Taxify (Taxi Mobile Application)

Regular street taxi will ask at least 5 manat for shorter distance drive in the city (during my short 3 days visit to Baku, I caught regular street taxis a couple of times, first one  - from the Baku Railway station wanted 10 AZN to get us to the boulevard, I managed to bargain down to 8 AZN).

Next time I was already smarter and bargained down from 10 AZN to 5 AZN to get from the Fountain square to the hotel at Flame towers. While in the third time street taxi took from me 7 AZN to take me from Flame towers back to the Fountain square.

Once I opened Bolt app I was surprised to learn I could do all those trips for 2-3 AZN only. 

Using Bolt we were able to get to Yanar Dag (Burning Mountains) and back (some 25 kilometers from Baku) for ~ 20 AZN (round trip) and to the airport (also about 25 kilometers from Baku) for ~ 10 AZN (one way only)

Bolt will help both to save and get on time on desired locations. 

Use my invite code GGSPN and get a free Bolt trip up to 10€. Redeem it at https://invite.bolt.eu/GGSPN