Divine magic is used by clerics, druids, paladins and rangers. For the most part, the distinction between divine and arcane magic lies in the story of how the magic is invoked — arcane magic derives from tapping into a "weave" of magic permeating reality, while divine magic is granted by powerful beings residing in the outer planes of existence. (The exact being can be specified as the caster's deity, or it can be left as some vague "power".) In terms of gameplay, the main difference between the two is that divine spells are never subject to arcane spell failure from armor and shields, even when the spell has a somatic component. There are also some differences in how spells become available (although this could be viewed as more a difference between classes than between types of magic), but otherwise the game treats arcane and divine magic identically.
Divine casters acquire access to spells based upon class level; they automatically know all of their class' spells up to a certain spell level. The highest spell level they know is the highest level for which their class level grants or allows spell slots. (Allowing spell slots without granting any is indicated by "0" rather than "-" in the class' "spells per day" chart.) While they know many spells, divine casters still need to plan their spells each day. Before resting, they need to assign spells to spell slots, which determines which spells can be cast the next day, as well as how often each spell can be cast.
All divine casters use wisdom to cast spells.