It is easy to get your own seeds from flowers. If the flower is allowed to remain withering, seed is created towards late summer. The art of getting good, pure seeds of flowers is largely dependent on what sorts your neighbour grows in her/his garden. The northern climate prevents some species as they do not have enough time to set seeds before the autumn rains cause the seeds to become moldy or the first autumn frosts destroy the unripe seeds.
The different species do not cross-fertilize, for instance Baby"™s breath cannot cross-fertilize with gypsophila despite being of the same family and species. However the different sorts of the same kind can do so more or less willingly.
A lot of them are basically self-fertilizing but despite that, insects are tempted by the beautiful flowers and manage to cross-fertilize quite a few of them. The sorts that cross-fertilize are of course, subject to much more mixing with other kinds. Luckily there is often only one sort of many common garden flowers.   
A boring way of preventing the insects getting at the flowers is to tie a bag over each flower or cover it with fibre-cloth and do the fertilization by yourself with a small brush. Despite these problems it is often easy to get good seeds from lots of flowers, as long as the seeds get enough time to ripen.  Harvest in dry weather when the seeds have the right colour, either by removing the seed collections directly in the garden or by cutting off the flower stems, hanging them up allowing them to continue drying indoors. Put something beneath to collect possible tumbling seeds.
Read more about the cultivation of seeds under "Grow your seeds yourself". You will also find advice under "Info etc." in the menu row.