First, conquistadors were not members of a formal Spanish military. They were members of privately organized companies (as in corporations not military units). As members of the company they would receive spoils according to their investment in the expedition (supplies, weapons, horses, war dogs, etc.)

Second, conquistadors tended to be of middling status. They had to have enough wealth to get to the Americas and join a company. But nobles rarely went as they generally had better opportunities for social advancement and wealth acquisition. Non-nobles tended to be trained in a trade. Some expeditions had sizable numbers of sailors who left the ships to join the expedition.

Third, most formal martial training was limited to the nobility. Otherwise, most soldiers learned on the job. This world be the case for conquistadors. Some would have had some training in swordsmanship or firearms (no muskets yet, only harquebus).

Diet and exercise, salted meat and hard tack or whatever they could get locally. Most successful expeditions recruited large numbers of native allies, greatly outnumbering the Spanish say times. Those alliances afforded them much needed supplies. Campaigning provided the primary exercise.

Restall's Seven Myths of the Spanish Conquest is a great primer on the conquest.