Hi,
You want the flowers to die completely and get brown. If you pick the dead flower too soon, the seeds will not be ripe. Hopefully, you get lots of blooms, so if you check on one and you picked it too soon, you'll have lots more to harvest seeds from.
The seeds are big chippy things, so at least they are easy to identify. The link below has a pic.
Remy

Here is a link that might be useful: Dahlia Seed Photo

This is great! It had never occurred to me to save seeds from my dahlia! I you let the flower go to seed, will the dahlia quit blooming? I am going to let a couple of flowers stay on the plant to collect the seeds.

Thanks for the info and pics!