Get permission to visit. usually they have transfers from ernakulam in kerala as far as i know. google u will get details. indian passport is enough. no visa required. since stay is less only limited people wil be allowed each date.
Best time to go is December to May, when it is cooler and drier. You require a special permit to visit Lakshadweep. The easiest way to obtain it is to book a package tour through the government's tour operator SPORTS or arrange a hotel to sort it out for you. Kadmat, Kavaratti, Kalpeni, Bangaram, and Agatti are some of the islands you must visit. You can also find a lot of information here: https://www.tripoto.com/travel-guide/lakshadweep/trips
Try to plan between December and May. It's the best time for traveling that particular place. Stay is limited there so find a government tour, they provide plan and organize there trips. And just ready your passport.