How to reach? Take any train that would drop you to Siliguri or New Jalpaiguri because you would have to go via road henceforth. It is an overnight journey, so plan accordingly.
After reaching there? If you're visiting a place that happens to be in the path of any of the common cities like Darjeeling or Kalimpong or is in the Gangtok route then boarding a public vehicle is not a problem. However, if you happen to be visiting an uncommon place, book a car beforehand or ask your hotel/travel agents to do it for you.
Stay? We always prefer a homestay over a lodge for the simple reason that it's a better way to get to know a family and just, feel like you're a part of their lives. And you're paying to be a part of someone's life :p
If you're new to the area, I would suggest that you contact a travel agent then you might come across newer things that you wouldn't if you were booking by yourself. It's perfectly fine if you were booking by yourself too as you'll find plenty of lodges and hotels in varied price ranges.
Something you should know: Alot of houses in the Icchey region accommodate guests. You probably wouldn't find their advertisements on the web but once you're in the region, you'll see signboards just about everywhere.
It's not a town or a city. Something like a habitat, an area that started being inhabited and now people are making a life out of the place.