While you can winnow the seeds as soon as the heads are harvested there is a risk that the seeds will be too damp to be able to store them safely. To avoid this, it is best to first bag dry the seed heads before winnowing them.
Bag drying also allows you to harvest the seeds a little earlier, which reduces the risk of the seeds becoming overripe and being blown away by the wind before you have a chance to harvest them.
Instead of crushing the seed heads in a bowl and winnowing them as soon as you harvest the seed heads, place the seed heads in a large paper bag and hang them up in a cool dry place for a couple of weeks to allow them to further dry out.
Once they are completely dry you can process the seeds as per the method explained in Saving Lettuce Seeds.
Any large paper bag is suitable, such as boutique shopping bags and Grilled burger chain bags. For large seeds such as beans or peas you can even use things such as onion bags.
LEFT: Placing ripe seed heads in a newspaper bag. RIGHT: Newspaper bags filled with seed heads hanging up to dry in my garage.
If you do not have a large paper bag handy you can make your own bags out of newspaper. To do this take a couple of sheets of folded newspaper, fold the side edges over and staple them together.
Making a seed bag using two sheets of folded newspaper