New drops can either be gained when killing monsters, opening chests or completing quests.
When it comes to drops from monsters and chests, they will be randomly generated from a loot table, which takes into account various factors, such as your characters current level, the monsters level and the monsters rarity. However there are some exceptions to this, for example particular monsters that need to be killed to complete a quest.
Quests that offer drops as a reward are also generally predetermined, rather than ones generated by a loot table.
Drops can vary between between gold, weapons, Armor, accessories and tomes.