Often the outsource it to places with cheap labour to grow fields of the crop and may have measures to control what pollinates them to produce the right variety. Many of the big global seed companies have been caught using child labour.
You can leave some crops to flower and seed to keep your own. If you are using hybrid seeds, then the seeds you get likely won’t match the parent.
Most veggies make seeds in the following way: first the plant grows and makes flowers (carrots are just the root of the plant), then insects pollinate the flowers. After that, depending on the plant, the flowers either turn into fruit (potatoes make poisonous fruit) which contain the seeds or they expose the seeds directly to be blown into the wind (carrots and parsely do this). Try putting a carrot in water and it will grow a stem with leaves which will eventually flower.
Somebody plants the plant and lets it grow until it produces seeds at the end of the season, then collects the seeds.
For your carrots example, this is what the [above-ground part of a carrot plant](https://i.ytimg.com/vi/Q233zFbFrYU/maxresdefault.jpg) looks like. From there [you get the seeds.](http://suburbantomato.com/wp-content/uploads/2011/05/Carrot-seeds.jpg)
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