Vladikavkaz has a small airport (OGZ) with connections to Moscow (Sheremetyevo and Vnukovo) and a few other Russian cities. Flights are reasonably priced and the most practical option for most visitors. By train from Moscow takes around 30 hours; several trains a week make the journey. By road the city sits on the route south from Mineralnye Vody, which has the nearest major airport.
Check current travel advisories before visiting. The security situation in the North Caucasus has improved considerably but some areas near the borders with Ingushetia and South Ossetia require permits or have restricted access.