Elista, the capital of the steppes is exactly the geographical center of Kalmykia located at the intersection of Tsaritsin-Stavropol and KizIyar-Astrakhan routes, two main ancient roads that crossed the Kalmyk steppes.
Bus
There are regular bus services to/from Moscow, Astrakhan, Stavropol and Volgograd.
Train
Trains go to/from Moscow and Stavropol.