Growing daylilies from seed is fun! Just keep in mind, they may look different than the parent plant, since daylilies don't come true from seed. You can pick the pods as soon as they start to turn brown or crack. There are a lot of different methods, but I'll share what has worked best for me.
Let them dry inside and remove the seeds.
Store the seeds in the fridge in a plastic bag with a bit of paper towel to prevent moisture. (Do not freeze.)
A couple weeks before the last frost is predicted for your area, remove the paper towel and put water in each bag. I mix in a few tablespoons of hydrogen peroxide per gallon of water to prevent rot.
Place all the bags in a tupperware container, in case of leaks, and put them back in the fridge.
After a few days or up to a couple weeks, you will see little white roots begin to sprout. When this happens, plant the seeds (careful not to break the tiny root) in a pot and grow them inside until all danger of frost has passed.
They can be moved outside whenever you are ready.
Make sure to keep them moist, but not soaking wet. It may take a year or two (or three depending on your location) for them to bloom, but when they do, it will be a surprise! You never know what you might get.