Let the flowers die naturally on the plant.... the flower petals will brown and dry up, the stems will go brown. Once the stems are brown it's safe to harvest the seed.

When they are ready to harvest, I just clip off the entire seedhead and drop them into a paper bag or open container. Put the bag/container in a dry place with the bag opened so that any remaining moisture will escape.

After the heads are fully dried like that, they can be stored in a sealed container if you choose -- and even in the fridge (in a sealed glass or plastic container/bag) if you want to ensure viability for as long as possible. Remove individual seeds at that time, or wait until you actually want to plant them. These guys aren't picky. I just rub the seedhead with my thumb to loosen and remove all the seeds.