Nearest railway station to Besant Nagar beach is Guindy, which is just 8.4 km. Although buses are frequent, but there is no direct bus available. So, you will have to change at least once.
Apart from buses, local autos are also available, they will charge you around 200 bucks.
If you have your own vehicle, then just put Edward Elliot’s Beach or Besant Nagar Beach in maps and you will be good to go.
Parking might be an issue, as it is a popular place. So, you will have to keep that in mind as well.