Taxis are available year round in Montauk.  There are fewer in the off season and plenty for the summer months.  You can easily find phone numbers online.  They tend to have bright colors and cute/funny names!  Beep Beep!  In the summer of '13 there were also free 6-8 person open "golf cart" type vehicles that were quite accomodating taking beach goers from/to the beach to hotels and even homes/shares within a specific area.  They seem to be advertising supported, and are communal/shared.  Taxis alway meet the trains and the buses and taxies are a must for trips to towns nearby to towns like Ammagansett and East Hampton to shop and dine, and when it is raining.  Taxi trips from the train or bus can be  shared as well.