Season: Of course the summer months, are extremely busy, but Darjeeling has something to offer all year round. Snowfall is probable in winter, but it is not guaranteed every year. Monsoons are beautiful in the hills as well, but be warned of transportation glitches.
Getting There: The nearest airport is Bagdogra, while Siliguri is well serviced by trains from Kolkata and other adjoining state capitals. After that, one must hire transportation to the hill destinations, most of which can be arranged by the accommodation in Siliguri, at optimal prices. Arranging transportation individually is possible as well, but I would personally recommend spending at least one night in Siliguri, (due to an overnight train from Kolkata :P).
Accommodation: There are a number of hotels in Darjeeling and Kalimpong, however, one must book in advance to be sure. While we had arranged our hotels via agents, online options are sprouting as well.
What to eat: Thukpa (hot meat soup) and momos- a delicacy. And of course tea is important to savor as well. The bakery is also good.