If you come from Germany, you can take a train from Trier to the station of Luxembourg-City. There are trains every hour. You have the possibility to get off in Wasserbillig and continue with the bus Nr 485 towards Echternacch or you remain in the train until Luxembourg-City and then take bus number 110 (direct) or 111 (passing over villages) to Echternach There are buses every 30 minutes to Echternach. There is also the possibility to rent a car at the station.
If you come from France, Belgium or Holland, you take the train to Luxembourg-City and then bus number 110 or 111 to Echternach.