Air
There are daily one-hour flights to/from Moscow (Aeroflot). There are also twice-weekly flights to/from Frankfurt (Lufthansa).
TrainFrequent trains link Kazan to Moscow’s Kazansky station (about 12 hours). Many also serve Yekaterinburg (14 hours, east), and Perm (17 hours). Besides, the railway station is a great attraction itself.
Bus
There are daily buses to Ulyanovsk (5 hours) and Nizhny Novgorod (8 hours).
Boat
It’s also possible to come to Kazan by boat, the route goes along a very scenic route.