Tea House/Homestay Trekking: If you are visiting the region as part of a larger trip and don't want to lug camping gear around with you for your whole trip, or are new to trekking in the Himalayas, Tea House or Homestay trekking is a great way to enjoy the region at a reasonable price and with minimal specialized equipment. Nepal is the most well developed and easiest place to Tea House trek, specifically the Evererst, Annapurna, and Langtang regions. Several treks in Ladakh can be done as Homestay treks, while in India, the state of Uttarakhand (formally Uttaranchal) probably has the most extensive system of trekking and pilgrim Lodges. However, in general it is usually possible to stay under some sort of roof anywhere there is a permanently inhabited village, although the availability and amount of food villagers will have available to share/sell will very from region to region and season to season. The great thing about this style of trekking is that it allows one to travel light and trek for long periods without carrying heavy supplies of food. Hiking with a light bag is particularly nice at higher altitudes where each additional bit of weight is magnified with increasing altitude. In the more specific case of Homestays, trekkers are provided a unique window into the cultural life of the people in that region as they eat and sleep in the same manner as the local family. Of course the disadvantage of this style of trekking is the loss in flexibility since the routes and stopping points are dictated by places where you can eat and stay. Another knock on this style of trekking especially in Nepal is that these routes tend to be the most popular and are therefore "too touristy" and "highways of trekkers." I don't believe this is a justified criticism, I've hiked some the most popular routes in the Himalayas and never felt this was a problem. The trails are long enough that you can usually space yourself away from the big groups, and if you want to see less people choose a less popular route. I enjoy this style of trekking and I feel the ability to travel light far outweighs any of the negatives.
Clothing (type depends on season and region), comfortable walking shoes or hiking boots, snacks (depending on availability along the route), map/guidebook, water bottle, water purification method, sleeping bag (recommended but not essential I trekked the Annapurna region without one just relying on blankets at the lodges), trekking pole or walking stick (not essential but often useful crossing rivers or going down steep descents), compass (if you don't have a good sense of direction), medical kit (tweezers, small scissors, bandages, antibiotics for diarrhea i.e. cyprofloxin, basic pain killer, cold/cough medicine, ect.)