Echternach is about 30 km northeast of Luxembourg City, roughly 35 minutes by car on the N1, or an hour by bus. The town has no railway station; the nearest railhead is Wasserbillig, 16 km southeast on the Mosel line from Luxembourg and Trier, and a regular bus connects Wasserbillig to Echternach.
From Germany, the town is immediately across the Sauer river — pedestrians can walk over the bridge into Echternacherbrück, which is a useful way in if you are coming from Trier (30 km east).
Within Luxembourg the bus network is free to all passengers, so getting to Echternach on public transport costs nothing once you are in the country.