Because of Grozny being highly devastated by years of war, transportation is often tricky and hard as much of Grozny's transportation system has been destroyed. However, since reconstruction began, it's possible to take a flight to the city or use a train, bus or the convenient highway system.
By plane
The only two ways to get to Grozny by air are by using the Vnukovo Airport in Moscow and the Sabiha Gokcen Aiport in Istanbul. Rusline is one airline with regular flights between Moscow and Grozny, and Grozny Avia is the second airline with the regular flights between Istanbul and Grozny, although it may be difficult if not impossible for non Russian visitors to gain proper authorization to travel there. The flights to Grozny are extremely guarded since the war and 9/11, so expect delays.
By car
Grozny is connected to the rest of Russia by a large highway system. The P-308, P-307 and M-29 highways connect the city to other cities in Russia. Keep in mind that it's best to take a map with you, or else you can get lost.
By bus
A bus usually leaves from Nazran to Grozny and other cities in the Caucasus region of Russia, so remember when you are going to stop.