If you are coming by air, you can fly into the Erzurum Airport, which has daily flights from Istanbul and other major cities in Turkey. From the airport, you can take a taxi or a shuttle bus to the city center.
If you are coming by road, you can take the E80 highway, which runs east-west through the city. From Istanbul, it is a roughly 12-hour drive to Erzurum. You can also take a bus from Istanbul or other major cities in Turkey to the Erzurum Bus Terminal, which is located in the city center.
If you are coming by train, you can take the Eastern Express from Ankara or Kars to Erzurum. The journey takes around 10 hours from Ankara and 3 hours from Kars.
Erzurum is also located on the ancient Silk Road, so it has a long history of trade and commerce. If you are traveling through the region, you may also be able to reach Erzurum by taking a local bus or shared taxi.