Even though it's at the far eastern edge of the country, getting to Narva is fairly easy. More than 20 express busses depart Tallinn's Bus Station (Bussijaam) each day, usually making the trip in 3 - 3.5 hours, depending on which bus you take. Tickets cost €10 - 13. You can find the complete schedule and price information at www.tpilet.ee. Once in Narva, you can get off the bus at the central Puškini stop, one stop before the bus station, which will put you almost directly in front of the Tourist Information Centre. Buses back to Tallinn leave from the Bus Station on Vaivara tn.
If you're travelling by car, head out of Tallinn on Peterburi tee and continue along the St. Petersburg highway (E20). You should reach Narva in about 3 hours.