Pictured above are the seeds of origanum vulgare.
These types of seeds are ready to be harvested when they easily shake loose from the stalk.
It's a fairly simple matter to go into the field collecting wind blown seeds with a brown paper packet held over the seed stalks to collect the seeds loosened by just a little shake of the stalk.
Just remember to label what you collect.
Fruits are a little different, generally requiring that you wait until the fruits are properly 'seed ripe' before you harvest them. That means more ripe than when you would ordinarily be comfortable picking and eating a fruit.
Some fruits can be tricky. Very hot peppers for instance, they can require careful handling. Anyone who has ever rubbed their eyes (or picked their nose ahem) can tell you this.
So we put the fruits into some water and let them soak until it becomes easier to separate the seeds from the fruit.
Saving seeds is of particular benefit to the urban organic gardener if attention is paid to selecting the best plants to harvests from, plants that did particularly well in the local environment. In this way, by a process of selection, the seeds you save from your garden will begin to produce plants most especially suited to your own particular local environment.