The seed has to ripen, so leave the pods on the plant until they dry out and turn brown. You'll know when the seed is ready to harvest because the little top cap will lift up, leaving an open space between it and the main pod. When that happens, cut off the pod, carry it to where you want new plants, then turn it upside down and twirl it around a bit. The seeds, which are tiny, should fall out. Or you can put them in an envelope and sow them whenever you want. You'll have the best chance of getting new plants if you sow the seeds in a spot that has been freshly cultivated. Papaver atlanticum is not long-lived but it is easy from seed and it usually self-sows, but again, the seed has to be ripe.

I also find that things like P. atlanticum will reseed most heavily if you scatter the seed over areas that are full sun, with a sandy or gritty soil texture and no mulch, and just lightly rake the seed in after you sow it. Scattering ripe seed in September is usually a sure bet to get new seedlings, but watch for slugs and snails. For me, almost all Papaver species that are said to be good self-sowers will do so on their own within gravel or decomposed granite pathways, where the conditions are usually perfect for them to get established without competition/shade from other plants.

Thank you both! This is exactly what I need. I'll stop dead-heading and look for the change in the seed-head.