Magic

 The two types of magic 

Arcane magic is used by bards, sorcerers and wizards. The important thing to remember is that arcane spells need to be learned before they can be prepared or used. Different classes learn spells with various degrees of speed and difficulty, but all arcane spellcasters need to learn a spell before they have access to it.

Divine magic, on the other hand, comes from the gods and is provided in full, and divine spellcasters have default access to all available spells for their class. However, they still need to meet the pre-requisites for casting a spell (have a spell prepared, have available spell slots, be able to cast spells of certain level, etc.) Classes with divine magic: druid, paladin, cleric, ranger.

 Spell slots and preparation 

Most spellcasters need not only to know spells, but to have them prepared beforehand in order to use them. Such a caster can only prepare a certain number of spells every day. This is the difference between "spells known" and "spells per day". When we refer to "spell slots", this means the available "room" for a spell to be prepared. A caster with three spell slots per day, who has already prepared ("loaded") three spells, cannot use any of his/her other spells, even if he or she knows them.

In gameplay terms, this means that each day you need to go through your list of known spells, and choose which ones to prepare, according to your available spell slots. You can "fill" a higher-level spell slot with a lower-level spell, but not the other way around. Also, if you have enough slots, you can load the same spell twice (or more).

Spell level and caster level

Material components

Scrolls 

Magic items; wands and rods; triggers

Detect magic, Read magic and Identify: which does what

Spellcraft checks