By train is by far the best option. ScotRail runs trains from Edinburgh Waverley to North Berwick about every half-hour during the day, taking 32 minutes. The line is a dead-end branch that terminates in the town, a five-minute walk from the High Street.
By car, take the A1 east from Edinburgh and turn off at the North Berwick junction onto the A198, about 35 minutes. Town parking is paid in summer but plentiful.
By bus, Lothian Country and East Coast Buses run from Edinburgh's St Andrew Square; the journey takes about 75 minutes and is cheaper than the train.
Edinburgh Airport is about 50 km away; transfer via Edinburgh Waverley by tram (or taxi) and connect to the train.