they are so beautiful and so many varieties.
you may find that after the flower finishes (cut it off right at the top near the petals, but leave all the leaves alone as much as possible) that when reforming the bulb and flower for the next year that there will be little bulblets also formed. it can take a few years before those bulblets will get big enough to flower.
high tech propagation of new varieties use cell cultures various hormones and growing mediums (i don't know anyone who does this).
the other method that more normal people can sometimes manage to increase numbers is to divide the bulb up cutting it in half, quarters, or even eighths (including parts of the basal plate) and to get those to grow, but it takes years after to get the plant large enough to flower again.
the problems (besides the time it takes to get big enough to flower again) is that in many cases you're going to lose some number of cuttings and many people don't have the space or patience to care for them for that long.
in my own case, my plans on cross-breeding and selecting new varieties of tulips came to a screetching halt because of diseases, predators, poor soils and general microclimate not being very suitable... so pretty much all i'm left with now are those varieties which are survivors (but they would not be if they weren't fenced). the dozens of varieties i planted extras outside the fence for a nice display for a season or two but eventually the deer, bunnies, etc. have reduced them to almost nothing and the daffodils have taken over instead. i did get some pictures before they got mowed down or faded away.