The town is small enough to walk, but there is a City bus, 1,60 Lei, get the ticket inside the bus.
To get around the Maramures area there is a informal shared taxi system. From Sighet east and south wait on Strada Bogdan Voda (between Carrefour and the ugly concrete Greco Catholic Church) until some car stops and asks where you want to go, if the direction is right he tell you step in (Bârsana 5 Lei, Monastery Bârsana 6 Lei), JAN Tour buses are also going from there, but i could not find a timetable. From Sigeth west wait at Strada Avram Iancu near Strada Vintea Pinteazu / Municipal Hospital (Sãpânta 5 Lei), there might be a bus from the bus terminal next to the Train Station, but i could not find it. Returning to Sighet stand anywhere on the mainroad.
There is a direct bus from Budapest, fridays only, 10 hours.
Every day a direct bus from Oradea at 14.30, takes 7 hours; from Clij Napoca at 7.00 and 15.00, 5 hours; from Satu Mare at 7.00 and 15.30, 3.30 hours; from Targu Mures at 14.00, 5.30 hours.
There are frequent minibuses from Baia Mare (and frequent minibuses from Oradea to Baia Mare)
The train leaving Budapest Keleti Pu at 16.40 is probably the most convenient, only 1 change of trains (Couchette until Beclean pe Somes), and the realy nice part from Beclean pe Somes to Sighetu Marmatiei in the daytime, total time 18 hours, waiting time in Beclean pe Somes 3.45 hours.
There are direct overnight trains from Bucarest and Timisoara with Couchettes.
You can also fly with Wizzair from several west european town to Cluj Napoca, from there by direct train, 6 hours arriving very late, or with change in Beclean pe Somes, but leaving Cluj Napoca at 4.58, or bus at 7.00 and 14.00, about 5 hours, the road from Baia Mare to Sighetu Marmatiei is also very interresting.
The Beclean pe Somes to Sighetu Marmatiei train doesn´t have Aircondition and it can get very hot in the summer, take enough water with you!
It's easy to get to Sighet. I happened to arrive by bus from Viseu de Sus (buses stop right on Piata Libertatii), but it was my departing train ride that was particularly memorable. A morning train ride through Maramures is, in my opinion, an experience that every traveler in Romania should not miss. Dorothy may have visited the Emerald City, but you'll get to see the Emerald Country! Maramures in the morning is a shade of green that you just can't see anywhere else, and as your train chugs along the tracks at a snail's pace you'll pass alien-like haystacks, horse-drawn carriages waiting at railway crossings, wood smoke rising from farmers' fields, and even churches rising mysteriously from the morning fog. The train moves slowly enough that you can peer out the open window (or the door, if you're brave and the conductor doesn't see you!), though even in the summer you should bundle up as the morning air can be chilly. Get ready for the ride of your life!