I pick as they develop and then the plant often produces more flowers over the summer. Don't know if that is what you are meant to do but as there are only 2/3 of us and I don't grow enough to freeze, it doesn't really matter to us.

The RHS says:
Pods are ready to harvest when they are well filled. Pick regularly or the plants stop producing flowers and pods.

Pick them as soon as the peas are sweet, fat & juicy. Don't wait too long, but you can freeze them to preserve the flavor. Yes it will produce more peas because the plants want to complete their life cycle. They will eventually run out of gas. One idea is to sow the seeds in 3 week intervals so that when the plants run out of gas, the others will still produce. If you grow Mange tout, you can eat the pods and all.