The two visual clues that I've picked up growing these plants is to first look for the color change. The seed pods on these poppies go from green to a purplish-brown color when the seed heads have dried.
How to Save Poppy SeedsUpdate: I recorded this video which is longer and explains it better than the original video below on how to save poppy seeds.
The second visual clue I've noticed is that the pods start to open right below crown in the area where I've highlighted with the arrow. Sometimes though the openings will occur before the pods have changed color and vice-versa so I make daily checks on the seed pods so that none will escape my attention.
By the time the seeds are ready to collect the stalks and leaves have turned yellow and I just pull them up and snip off the seed heads into a paper bag and allow them to completely dry out before emptying out the seeds. To empty out the seeds I find it easy to just place the pod upside down in a paper bag and tap it a few times so the seeds spill out. When I have smaller seed pods it is easier to just crush the head and remove the chaff later.
Updated: New to saving seeds? See How to Save Seeds for general tips and information on saving seeds from your garden for next year.
How to Transplant Poppy Seedlings in the Garden
How to Sow Poppy Seeds
Garden Video on how to collect poppy seeds in your garden