There are basically two different methods to collect seeds the Dry Method and the Wet Method.
This is the most common method of collecting seeds. It involves crushing mature seed heads and extracting the seeds either by winnowing crushed heads or picking the seeds out by hand. For a detailed explanation of how to winnow seeds see Saving Lettuce Seeds.
Vegetables that you would use the dry method to collect seeds from include Lettuce, endive, carrot, brassicas (cabbage, broccoli Cauliflower etc..), leek, onions, capsicums, chillies, eggplant beans and peas.
This involves washing the seeds in a sieve with a jet of water before tipping the seeds out onto newspaper to dry. For a detailed explanation of this method see Saving Tomato Seeds.
The main vegetables that you would use the wet method to collect seeds from are tomatoes, pumpkins, zucchinis and cucumbers.