Train
Daily trains run to/from Moscow’s Kazanky station, the way usually takes about 13-14 hours. There are also daily trains to/from Ufa. You may also get to Penza be a transit train following from Bishckek to Mosocw, from Vladivostok to Kharkov, from Adler to Novosibirsk and from Chelyabinsk to Odessa.
Bus
There are regular buses running from Penza to Moscow, Samara and Tambov, as well as a wide range of local bus services.