Narva is connected to Tallinn by train and bus. Trains usually take around three hours and arrive at Narva station, a walk or short taxi ride from the castle area. Buses are frequent and useful if the train times do not suit.
By car, the E20 highway runs east from Tallinn through Rakvere and Jõhvi to Narva. The Russian border crossing is in the centre, but check current border rules carefully before assuming you can continue onward.