Especially from early times, arms were "assumed", or adopted by the men themselves. The profession of being a herald arose about the same time as heraldry itself, so that could have been a source of knowledge. But heraldry is an art style -- some motifs were common, some were uncommon, some were not done -- so men may have chosen their designs themselves based on what they saw around them.

Arms could also be granted by a lord or by a king. In places with stronger authority and an interest in doing it, such authorities could grant such arms, or forbid men or corporate bodies from assuming arms. In England, that started in the 1400s. In other lands, like Norway, it never happened.

As for "how did the symbols get selected": I don't know of sources before modern times explaining the reasons for actual designs. There were a lot of heraldic treatises explaining the symbolism of this and that, but they also often talked about practices that never happened (abatements of arms, for example), so here, have a large grain of salt to take them with.

Some inferences have been made. The obvious case, a common one, is to pun on a hereditary surname (in heraldry, called "canting"). (Why on the surname (last name, family name)? Because arms were hereditary, and given names (first names, personal names) usually weren't except by family custom, so a pun on the given name would be lost in a generation.) The Lucy family in England bore three lucy-fish (apparently an alternate name for pike). The Dauphins of France bore a dolphin. Shakespeare had a spear on his bend. Castile and Leon, in what's now Spain, bore respectively a castle and a lion.

Another obvious case is cadency: a younger son in England and other such jurisdictions taking his father's coat and making a change to make it similar but not identical.

I have heard that arms might also be influenced by the lord's arms, that there's an unusually large number of arms in Brittany that had ermine (the arms of the lords of Brittany were "Ermine").

There were also local styles, but the examples that come to mind first might also be due to influence from the lord. Purple tended to be more common in Spain (but was that because the arms of Leon later tended to be purple?). Eagles are the most common animate arms from Germany east (but was that based on the arms of the Holy Roman Emperor?). A black animal or charge on red was far more common in Germany. A green hill or trimount on blue, usually with something atop the hill, is extremely common in Hungarian armory.

But in sum, in a lot of cases, we can't say why.