The brassica family includes broccoli, cauliflower, kohlrabi, rocket, cabbage, kale and turnip. To produce seed you need to allow one or more plants to flower. The flowers will then form small seedpods which need to mature. Once they become brown and dry they can be collected and opened into a small bowl were the seeds are tiny and black in colour.
Saved brassica seeds lasts up to 5 years in ideal storage conditions (dry, cool and away from direct light). Note that for broccoli and cauliflower the edible portion is the unopened flower heads so if you are wanting to save seeds of these plants you will not be able to eat all the florets. For root vegetables like turnip by the time the seeds are mature for harvest the vegetable becomes extremely woody so set aside one plant (a particularly good one to breed good qualities) that is only for seed saving and not eating. Seeds from this family should be used within 3-5 years.