The LIRR from New York Penn Station is an easy traffic-free way to travel out east. They run 2-3x per day with travel time under 3 hours. The best train station options are: Southampton and Bridgehampton.
The Jitney is a Hamptons bound bus that runs from the east side of Manhattan to various towns in the Hamptons. As our wedding is in the off season, traffic should be light, making the Jitney an easy travel option. Details and schedules can be found at https://www.hamptonjitney.com
While driving out east is a simple option, we recommend planning accordingly around rush hour traffic if you are driving out Friday night.
There are also plenty of Ubers and Lyfts in the Hamptons for your use throughout your stay.