propagating Gloriosa lilies

Those extraterrestrial-looking flowers on the left are Gloriosas.  These are large (perhaps 5" across) lilies that grow on climbing vines to 8 ft long.  The vines cling to any objects they encounter with pealike tendrils.  Even in very indirect light, mature vines may produce six or more flowers each.
The flowers show a nifty evolutionary trick that decreases or eliminates self-pollination and increases "outcrossing", which is cross-pollination of genetically different members within a species.  This increases genetic diversity and thus genetic health of the population.  In Gloriosas and some other flowers, self-pollination is nearly impossible because the female receptor for pollen, the style, is longer than the stamens and bent away from them.
There are two caveats when it comes to Gloriosas: first, cross-pollination of different flowers produced by a single tuber does not constitute outcrossing; the flowers are all genetically identical.  Furthermore,  when you raise captive Gloriosas, if you obtained the plants from a single source they are likely to have been vegetatively propagated and all the tubers will thus likely be genetically identical.
That's okay: Gloriosas are self-fertile (will produce seeds once the mechanical barrier to pollination is overcome, regardless of genetic identity of the parent flowers.)
Because of the nifty style arrangement, if you want these flowers to produce seeds, you will usually need to hand-pollinate them.  This is easy to do when pollen is ripe (it will appear as a fluffy powder on the ends of the stamens).  Use a water color brush to move pollen from the ends of the stamens (anthers) to the tip of the style (stigma).
When you see a bulge forming below the now-dead flower, you know that seeds are developing.  Wait until this pod becomes brownish and papery and begins to split, the seeds inside it dark red.  You can then collect the seeds and plant them.  They are stony little things, and germination may be enhanced by nicking them gently or rubbing them a little with sandpaper.  Plant in moist medium (seed starting mix or potting soil).  Bottom heat is ideal, though probably not essential.  Germination proceeds erratically over a period of at least six months.
Grow your seedlings in very well-drained medium kept somewhat moist.  Tubers will develop under the soil, and these tubers will enlarge with time.  You will get relatively short, slender, flowerless vines, then long slender vines, and gradually the vine stems will thicken.  When the tubers become large enough, usually after several years, they will be sufficiently mature to produce flowers.