Needless to say, any kind of seeds you recycle need to be heirloom.
Radish seeds are super easy to recycle and you don't need a long growing season.
Plant the radishes early on in the season, and simply let them grow. The plants will get very big and form white flowers.
After the flowers disappear, they will form seed pods.
Let them go for as long as you can, until they are filled in and dry.
You can 'dry' the seeds in the seedpods. Just spread the pods open on some newspaper and leave them there for a couple of weeks, or longer.
I usually take the seeds out of the pods during the winter months since there isn't too much time to do it during planting season.