You can get to Narva via Tallinn
There is no airport in Narva. The closest and the main international airport in Estonia is Lennart Meri Tallinn Airport. The airport is at a close distance to Tallinn city centre and accessible by public transport (bus No 2 and tram No 4).
There quite fast ferries Megastar and Star getting from Helsinki to narva in two hours. Up to six daily departures all year round.
and then from Tallinn to Narva by haighway E20 or railway
There is rather good bus connection between Tallinn and Narva. The travel time is usually 3h15min and the ticket costs between 7-15 euros. You can look up the timetables and buy tickets online www.tpilet.ee.
Direct train connection is only possible between Tallinn and Narva - no direct trains from Tartu (change in Tapa). The travel time is 2h15 (once daily express) or 2h45min (regular train) and the ticket costs between 11-16 euros. You can check the timetable and buy tickets online www.elron.ee.
It is best to take the train from Ülemiste station, near Ülemiste shopping centre, a 15-minute walk and a few-minute taxi ride from the airport.
If you have more time, Tallinn Central Train Station - Balti jaam in Estonian - is located near the old town. By taxi from the airport, it should take around 15 minutes, but it very much depends on the traffic, in the morning and evening rush hours it can also take 30 minutes or more. In regular circumstance the taxi should cost around 10 euros.
You can get to Narva from St. Petersburg by haighway A180, railway on by plane via Tallinn
When in Narva
In Narva, the bus station and the train station are right next to each other.
You can call a taxi, all taxi rides inside Narva are 2.50 euros (if you take a waiting taxi from the station, it costs more!). Taxi numbers: +372 50 44444 (Ida Takso), +372 55 906090 (Seti Takso), +372 59 696969 (Gold Takso). Beware that taxi companies and drivers tend to speak only Russian.