Montauk is easily accessible by car, by rail,and even by boat.
Taking a plane to New York is easy. There are three airports to chose from in the region. John F. Kennedy Airport and LaGuardia Airport, both in Queens, and MacArthur Airport in Suffolk are all easily the first step to getting to Montauk.
Either travelling in your own car or by rental car it is easy to get out to "The End". The only road that goes out to seaside town is Sunrise Highway (or Route 27), which runs from New York City all the way to Montauk. Along the way Sunrise Highway turns into Montauk Highway yet it is still known as Route 27.
The Long Island Railroad (LIRR) is an alternative to driving. It too runs from Penn Station in Manhattan to Montauk.
There are also places at which one can dock their boat and also ferries that run from other East End locations.