Each bulb produced a single stem at the top of which is a "flower" that is actually composed of several small flowers.
After the bees have done their job you'll notice the green center of each of these tiny flowers begin to swell as the seeds begin to develop inside the seed pod.
The petals wither away leaving only the seed pods that turn from green to an olive color as the seeds grow inside the little pods. Inside each pod you'll find between two and three seeds forming. If you're worried about your Allium seeds being eaten by birds or falling off you can cut the stem and bring it indoors once you see the first signs of the pods splitting open and revealing the seeds inside.
Leaving the pods to mature further in the garden will lower the number of seeds you can collect from your Alliums but with each "flower" producing dozens of seeds this isn't really much of a problem. Even if you leave a stalk in the garden during the whole season by the end you may still find one or two seeds hanging on.
Collecting Allium Seeds Garden Video
If you're worried that the seeds will fall off you can cut the dry flower stalks and place them upside down in a paper bag to dry. As the seed pods dry they will crack open release the seeds inside the paper bag.
Once you know how to collect Allium seeds in the garden you'll have to do it twice every garden season. In the late spring you can collect seeds from Alliums like 'Mount Everest,' 'Purple Sensations,' 'Gladiator' and in the late summer and early fall you'll be have to save seeds from nodding wild onion (Allium cernuum). The seeds look identical in most of them so make sure to label them to keep track of them. Although, I find that nodding Alliums seem to have shinier seeds than the others. When you sow Alliums seeds you will only get seedlings the first year and it can take a couple of years before your Alliums mature enough to bloom.
See my post on How to Save Seeds. In it you'll find tips for the beginner gardener who would like to save seeds.