By planeRussian airlines Aeroflot and S7 are the main (and safest) airlines offering international transfers to Kazan. Air France and Etihad Air also offer flights to Kazan via Moscow (Domodedovo Airport). Flights from Moscow take around 1 hour and the airport is a 30 minutes drive from the city centre. Taxis from/to the airport should cost around 600-800Rbl.
There is also one direct flight to Kazan from St. Petersburg at 23:30 although all of the above mentioned companies offer connecting flights via Moscow.
By trainMoscow and Kazan are well connected, with eight or nine trains every single day. The journey is a relatively swift 11 or 13 hours (depending on the train you choose), and most traverse the country in the evening. Only one direct train connects St. Petersburg and Kazan, a journey that takes 22 hours. Be aware that there are two stations in Kazan, but Kazan-2 is largely used for transit purposes.
We recommend you two convenient trains: №002Й (20:48 - 08:00) and №024M (23:08 - 10:45).
From St. Petersburg there is only one direct train a day which leaves from Moskovsky station (metro Pl. Vosstaniya). The journey takes approximately 22 hours and leaves St. Petersburg at 15:30 arriving in Kazan the next day at 13:58.