In 5E, spell slots are based on a character’s class. Each class has a number of spell slots per day, which is determined by the character’s level.
For instance, a 3rd-level wizard has three spell slots per day.
Wizards also have access to a number of bonus spell slots, which are based on their Intelligence score. These bonuses are not counted towards the daily limit.
A player can cast any spell they know without expending a slot, but they must meet the requirements for that spell (such as level required, casting time, and so on). When a player casts a spell that requires a slot, they must expend one of their prepared spells or coins to use that slot.
If they have no prepared spells or coins left in their wand or pouch, they must spend an action to retrieve a spell from their library.
A player can have up to five active spells at any given time (three if they have the Extra Attack feature). If they cast one of their active spells and then cast another active spell within the next minute, the new spell will overwrite the old one.
If the player doesn’t cast an active spell within 1 minute, their currently active spell will expire and be replaced by the first Active Spell from their list of three.
