My second favorite genus of carnivorous plants, there may not be anywhere near as many species here as there are in Nepenthes but oh how you can play with the localities and complex hybrids...and the results are in some ways even easier to see when you start messing with growing them up from seed.
There are more registered cultivars of American pitcher plants than nearly any other carnivore genus out there (excepting perhaps the Venus flytrap...), and many of the best new ones have arisen from careful horticultural control of crosses between promising parent material. Every batch of seeds, even of hybrids that have been done before, can produce something entirely new and potentially worthy, and as with any other group of plants it presents the potential for easy means of getting a lot of plants much more cheaply than getting divisions. Seeds are also sometimes easier to acquire rare plants through; while you still can only sell them between states with a federal permit, the three endangered species can be gifted, and seeds tend to be easier to gift than big plants. It's not without its own challenges however.
Producing Sarracenia seed is fairly straightforward: each flower has five stigmas on the inner tips of the umbrella-shaped upside-down style, and all it takes is rubbing pollen on them while they're receptive (which is a period that lasts at least several days). Whether you want pure species, hybrids, or even selfings, it all works the same. The ovary then ripens over summer, turning brown and releasing up to several hundred seeds in later summer through fall. If kept at room temperature, viability can be lost after a few months, but kept dry and fridge-stored, these seeds can last for at least a couple of years (from personal experience there seems to be a bit of a toss-up on whether they start losing viability after that or can be maintained long-term).
The first challenge with seeds is, because these are temperate plants that release their seeds late in the year, they are primed to experience a cold dormancy period in the soil before they will germinate. While you can try using germination inducers like gibberellic acid to convince them to sprout, it's easy to misjudge the concentration needed and I personally am not quite sure what strength of the chemical the seeds actually require in order to sprout. Too much will kill the seeds instead, or result in them sprouting lanky and weak.
The easiest method, is a simple cold stratification. Seeds can be sown on the surface of a pot that you intend to grow them in which is set in a cool place either over winter, or for a few weeks in a refrigerator. Or, the method that I use, is that seeds can be wrapped between layers of moistened paper towel and sealed in a small plastic bag, which can then be set in the fridge for the necessary time. For most seeds, the obligate stratification period is only 4 weeks; some of the mountainous species like S. oreophila, jonesii etc. may do better with 5-6 weeks, and forms of S. purpurea from very cold northern regions such as Canadian localities may need up to 8 weeks of stratification. Anything beyond this is facultative; the cold will keep the seeds dormant, but the germination inhibitors have already broken down and the seeds are simply waiting for spring. If the baggie method is used, once stratification is over, simply pull them out and scatter them over a suitable soil mix (most Sarracenia do best in something peat-based, depending on your watering a 50:50 peat/perlite or sand, or higher sand content will work).
Once the seeds have stratified and are sown on soil, keep them moist, to even wet. Additional humidity is not a need unless you live in a very dry or windy place apt to dry out the soil surface rapidly between waterings, as the seeds need constant contact with water in order to sprout, and warm temperatures (above 60 degrees Fahrenheit preferably, 75 or higher even better). Growing indoors is generally safer, less risk of wind or rain causing the seeds to be lost and conditions can be more easily controlled for best growth. They should not be covered with soil either, but have access to light. Germination typically occurs within 2-4 weeks, though some seeds may take as long as a couple of months (these are usually outliers rather than the norm). The seedlings are dicots, producing two slender round-tipped cotyledons that unfold from the seed, and may stay with nothing more than this for a month or two as they photosynthesize and prepare to produce true leaves. The first true leaves will be mini pitchers, only an inch or less tall usually and nearly all species look similar to each other at this stage.
Taking care of the seedlings will present the next set of real challenges; they need light, and a LOT of it. Like their parents, they need nearly full sun to not be etiolated, and to get them growing fast they need nutrient sources. Some people will spray them or soil-drench with dilute fertilizer, though be careful with these methods; Sarracenia are far more tolerant of nutrients in the soil than many other carnivores (and in fact can benefit from it, especially if simultaneously getting fed via pitcher), but seedlings can quickly be overrun by fungus or algae if nutrients are allowed to build up or remain. If fertilizing this way, leave it in the soil for them to absorb for a day or two, then flush the pot or tray to remove excess. When you have many thousands of seedlings, this is generally the most effective method.
For fewer seedlings, try feeding the pitchers directly. Small needles are very effective for getting liquid fertilizer into the pitcher mouths when small, and once pitchers start getting a couple inches tall they're usually big enough that pipette dropper tips can fit. Feeding them this way avoids algal issues, and can boost growth quite rapidly. Feeding once every couple of weeks will ensure rapid growth for most (some, like S. oreophila, will be slow no matter what you do though). Expect though that "rapid" is still relative; generally, seedlings will take 8 months to a year to begin displaying mature traits when heavily fed, and may take 1-2 years on a more reserved routine.
The first year of a seedlings' life, you can usually skip winter dormancy without issue; this allows for continual growth and more rapid maturity if growing indoors. If there is a space for it you can also leave them under 24 hour lighting for the first year or so as well for increased development. After this point however, once of sufficient size to have a visible rhizome starting to develop, seedlings should begin being acclimated to an outdoor environment where they will grow best (or a greenhouse space if that's what you're using). If transferring from artificial light to full sun, you may see present leaves burning as they are exposed to stronger light, but given a couple of weeks new acclimated growth should develop and the plants will settle in.
At all stages, make sure that you are giving your seedlings plenty of room to grow; a crowded pot will result in a couple of particularly robust plants (for those particular conditions) outgrowing the rest, and a few being shaded out and dying. If you find seedlings crowding each other, repot and spread out so they all equally have access to light and root space. Remember that Sarracenia develop quite significant root systems as well; even a new seedling with only one or two leaves might already have a root half a foot long. Deep pots with good aeration help them develop strong roots. Once seedlings start acclimating to their final growing environment and display mature traits, you can start choosing which ones to keep (as you almost certainly won't be able to keep them all, especially once you get to the point of working with hundreds or thousands of seedlings). If you can, don't cull plants until you've seen at least somewhat mature traps, as it sometimes can take until almost flowering maturity before Sarracenia will display their true colors (this may be anywhere from 2-5 years of age). The drabbest little seedling at the start might just end up being the flashiest one once it's 2 feet tall.
Lastly to remember: failure is ALWAYS an option. Sometimes some seeds just aren't any good, and there's not much that can be done to control that. Or, some seedlings may just end up weak growers and die off. This is why working with seeds is a gamble no matter what kind of plant you're working with. There's risk...but also great reward when things do pan out as hoped.