I see allium seed heads amongst the Icelandic poppies.  I leave the seed heads alone and find I get self seeded alliums popping up all over the garden.

I have grown bulbs from seed though and the process is much the same for all of them.  Cyclamen are a bit more tricky and need extra stages, but the main trick to all bulb seeds is to keep the baby plants in active and healthy growth for as long as possible to bulk the bulbs up.  Wait until the seeds are dry and ripe, then cut the whole seed head and put it into a paper bag or plastic tray for the seeds to drop out. 

Sow the seeds in a decent sized pot in soil based compost (John Innes) and top the pots with fine grit. The grit is important as it keeps moss and algae from taking over the surface.  Keep them outside, but somewhere a little sheltered for the first winter.  I have used a cold frame successfully but you could just rig up a couple of bricks with a sheet of glass over them.  You want to avoid sodden soil conditions. 

You should get seedlings the next spring - allium seedlings do look like blades of grass so be ready for that.  Make sure you keep the pot watered and feed it as well.  Tomato food is fine while you are doing the greenhouse stuff or any liquid plant feed you have to hand.  A little and often is the best.  After the first season, you should be able to tip the pot out and find small bulbs have formed.  You can plant these out but they will not flower for an least another year.  If you want to carry on in pots and lavish care to speed things up, space those bulbs out over several pots and repeat the process.