Arriving to the city.

If you come abroad, there are Lufthansa flights from Europe.
If there's need to get from Moscow, there are flights, train and bus.
Comparing plane and train from Moscow, I would advise train. It would take less time and more comfortable schedule.
Nizhny Novgorod is 6 hrs by day train or about 8 hours by night train or by bus from Moscow.
Train takes:

• 1 hour from hotel to station;
• 6 hours in train;
• 0,5 hour from station to hotel.

All together 7,5-8 hours.
As to schedule, you would arrive at 8-9 p.m.

Plane takes:

• 1 hour by underway;
• 1 hour by bus or train to the airport;
• 1-2 hours waiting and registration;
• 1 hour flight;
• 0,5 hours to get a luggage;
• 1 hour to hotel from airport.

All together 5,5-7 hours, and you would arrive at 11 p. m.

I would dare to recommend to take some lessons of Russian before arriving to town, or find a person who would follow you here. It isn't always possible to find someone English-speaking at the streets.