Saffron purchased at retail is monstrously expensive: around $44 for a quarter-ounce. But, amazingly, it's easy to grow in the home garden. (What makes it expensive at retail is not any difficulty in growing the plant--it's just a variety of autumn crocus--but the hand labor required to harvest the spice itself in quantity; but in quantities suited for household consumption, and for occasional much-appreciated gifts, it's no big deal.)
Saffron crocus bulbs are now available from several well-known home-garden seedsmen, who usually ship at the right time of year for planting. The bulbs you receive should be about the size of a healthy garlic clove.
There are only two easy "secrets" to readily growing your own saffron: 1) do not let dormant bulbs get materially wet, much less sit in wet ground; and 2) harvest timely. (We'll elaborate below.) A Spanish commercial saffron-grower's web site says "The cultivation of saffron needs an extreme climate; hot and dry weather in summer and cold in winter." Sound like any place we know?
Modern saffron is entirely hybrid and does not set seed at all--all propagation is vegetative. "Cultivars" are very rarely mentioned by home-garden seedsmen in connection with saffron, though there are certainly plenty enough out there; one, Crocus sativus 'Cashmirianus', is said to be an especially fine producer in northern gardens (we could only find one vendor, about 50% more than plain saffron crocus bulbs).
What is most important, however, is that you buy bulbs only from a reputable seed house, making quite sure that what you buy are saffron crocuses, not autumn meadow crocuses (sometimes confusingly also called saffron crocuses); be utterly sure you are getting real Crocus sativus, not Colchicum autumnale.
Your chosen seed house will probably send you the bulbs at the right time anyway, but the best time for initial planting is in early fall, typically about the start of September for our area; bulbs planted then ought to bloom (and thus provide a harvest) in the autumn of the immediately following year.
Saffron's life cycle is like this: in the autumn, it puts up leaves (which look a lot like a vigorous clump of grass), which continue to grow through the winter, often reaching 18 to 24 inches; in spring, around April, that portion of its annual cycle ends, the leaves die down, and the underground bulb goes "dormant"; then, with the return of autumn, the bulb breaks dormancy and sends up new leaves, then its flowers, and the cycle starts over. We need to know this because the one thing that will for sure kill off saffron is having its bulb stay damp for any nontrivial amount of time during the plant's dormant period. If a dormant saffron bulb sits in wet soil, it will very quickly rot completely away, leaving naught but a damp husk for the puzzled gardener's probing fingers to find. So from roughly April to September (more exactly judged by the plant's actual performance), it needs to be in dry soil.
(Naturally, there will hardly ever be any autumn flowers in the very year you plant.)
Gardeners worried about winter low temperatures can keep the containers indoors till the worst of the winter is past, but that is probably unnecessary in our climate (it is considered reliably hardy to at least Zone 6, -10° F.).
Around here, we get about an inch of rain a month in May and in June, often in the form of heavy storms: that can be fatal to outdoors saffron. Thus, we are best to plant our saffron bulbs in some sort of container (or containers: we use two 1' x 2' boxes for two dozen bulbs) that can be moved from indoors to outdoors twice a year without herniating.
Courageous souls can try growing them in ground outdoors; the crux is making very, very sure that your soil has superb drainage--a south-facing raised bed might work. They are, of course, perennials, so wherever they're set is where they'll be forever. Or one can try growing them completely indoors, but reports suggest that they do not perform as well without some outdoor time.
As to how many bulbs to plant: You should get three threads from each saffron plant. Experienced cooks will generally know how many threads they're likely to use in an average year, but for a rule of thumb figure on three threads per person for a main dish flavored with saffron (so, as an example, a family of four having a saffron-spiced dish on average once every couple of months, 24 plants would be needed: 3 threads x 4 persons x 6 meals a year / 3 threads a plant).
The planter-box soil should be rich, fairly sandy, and--above all--well-drained. Plant your bulbs 2 to 3 inches deep and the same 2 to 3 inches apart.
Crocuses do not need all-day sun, but they should get at least several hours a day. When they are in their growth stage (but never while they're dormant), water them lightly every other day. Cultivate shallowly with a light hand if weeds poke up.
When leaf growth emerges in the autumn, harden the plants off, then set them outside, preferably in a spot not only sunny but somewhat sheltered. They can tolerate a lot of cold, so the hardening-off need not be terribly prolonged: just avoid shock. In the spring, start keeping a close eye on them; when the leaves start dying back, probably in April, stop watering and bring the plants indoors for the summer. Again:do not water them once the spring leaf die-back begins.
In the autumn, the plant will break dormancy and leaves (with flowers soon to follow), will start coming up. When the first new leaves emerge is the time to reinstitute watering, harden the plants off again, and move them back outside.
The other "success secret" to growing saffron is harvesting: you've got to watch the plants daily at the right time of year and harvest from each the day it's ready--you cannot put this off and get satisfactory results. Each flower yields three stigmas (filaments or threads), which dangle from the throat of the flower. If the stigmas are not picked on the day the flower opens, or the next morning at very latest, they start to deteriorate. (Typically, new leaves appear in early September and flowers in early to middle October, but Nature follows her own calendar each year.)
When you find a newly opened flower, wait till any morning dew has thoroughly evaporated, then cut the flower. Remove cut flowers to a convenient work area--say a well-lit kitchen counter--then take a pair of tweezers and gently and carefully extract the three red-orange filaments, or threads, that you find in it--each of which should be about an inch long. Have a a secure container for plucked threads (ideally a small bottle) ready to hand, lest any blow away.
Keep watching your crop even after all bulbs have yielded a flower: it might happen that you get lucky and get a second, or even a third flower from a given bulb.
It's also important to thoroughly dry harvested threads before bottling them up for storage. Some sun-dry them (taking due care that the ultra-fine threads can't get blown away). Others use applied heat, which is OK if it's gentle heat applied over some time--remember, we want to dry the threads, not roast them. Perhaps the easiest technique is to lay them on a paper towel, with a sheet of glass or clear plastic over them to keep them from blowing away, then leave them on a sunny countertop for a while.
Saffron bulbs multiply readily, and can (and probably should) be divided every few years. Applying a small amount of balanced fertilizer annually when the bulbs break dormancy will be beneficial.
Besides any links presented above on this page, the following ought to be especially helpful.
Saffron - from Gernot Katzer's immensely valuable Spice Dictionary
Plants For a Future Database: Saffron - lots of data on the plant, and links to yet more
The Truth About Saffron - extensive review of its biology and taxonomy
Saffron -- Crocus sativus (PDF) - Crop and Food Research, New Zealand
"Richland man specializes in spendy spice" - a 1997 article from the Tri-City Herald newspaper about an eastern Washington amateur saffron grower (now only at The Wayback Machine site)
Saffron Cultivation - good general discussion of its growth needs