To get to Erzurum from the airport, you can get helpful guidance on-site. The most common option is taking a taxi. The distance from the city to the airport is approximately twelve kilometers. You can also take a regular city bus, which stops near the airport exit.
Additionally, the bus makes a stop near the international bus terminal in the city. Taxis are more expensive, but they will conveniently take you wherever you need to go. What will please any tourist is that the taxi drivers here are friendly, exceptionally polite, and ready to provide any information you may need. So, the choice is yours. The cost of a taxi ride can reach up to 50 USD.