TROPICAL PITCHER PLANT
Nepenthes
Nepenthes are also known as tropical pitcher plants, and in my experience, are the ones that most people recognize when you mention pitcher plants. There are a lot of different species (over a hundred), and they tend to grow in humid rainforest environments. This can make some varieties challenging to grow at home unless you have a greenhouse or other humid indoor environment.
However, there are some that are fairly easy to grow - Nepenthes ventricosa is considered a good beginner plant and can be found at many local plant nurseries and can be grown in a sunny spot indoors or in a terrarium (or in a greenhouse).
Many carnivorous plant enthusiasts grow some exotic varieties, like the ones you might find in Borneo, and they can be extremely expensive and challenging to grow.
An additional challenge when trying to grow Nepenthes is that it is tough to propagate them from seed. You need to find a male and female plant that are in bloom at the same time, which is quite challenging, even if you aren't limiting to the same species. A lot of the serious growers utilize tissue culture to grow these plants, which is quite an investment. One day, I might consider looking into it.
SOIL
I think a mix of two parts sphagnum moss to one part perlite works best. Pure sphagnum can be used too.
DORMANCY
These are tropical plants, so no dormancy is needed. The highland varieties like a drop in temperature at night. The lowlanders can take it but don't need it.
WATERING
If the plants are in a place where it won't dry out quickly, then a tray is not needed, and the plants can be top watered. If inside, however, then put in a tray of water, but let the water evaporate before adding more. They don't like to be sitting in water for long periods of time. They do like misting though.
PROPAGATION
There are three methods of propagation. Seed, basal offshoots, and stem cuttings. Nepenthes have male and female plants, and you'll need two of opposite gender to be flowering at the same time to have a successful pollination. I like to snip off one of the anthers on a male plant, then brush that on the stigma of a female plant. The second method is by basal offshoots. When a plant gets big, it will sometimes produce a small plant from the bottom area of the stem. Let this grow for a little, as if cut off too early, might not survive. I would wait until a 4 inch leafspan minimum. Cut it off (it feels horrible at first) as low as you can get to the stem. Then press it into the soil (it shouldn't have roots). Make sure it has high humidity and is wet because it doesn't have roots. If the leaves look wilted, it is okay as long as the middle has a growth point. The third method is by stem cuttings. After a while, a mature plant will start to vine. The gaps between the leaves will get really big. What you can do is take cuttings of the stem (minimum 2 leaves each), cut the pithers off and cut the leaves in half to save water, then stick it in some sphagnum moss. Make sure it has high humidity. After a while, a new plantlet should form right on top of where a leaf and the stem connect.