From D&D 3.5 to 5.0(5E) - 16 - Spell Slots for Wizards

The big change for wizards is the use of spell slots.  Just as in all previous editions of D&D, wizards will learn spells and record them in their spell books, but each day the wizard will only be able to prepare a few of those spells.  The number of spells that a wizard can prepare is the sum of his spell level and his intelligence ability bonus.  So a 3rd level wizard with an Intelligence of 18 could prepare 7 spells a day, 3 for being 3rd level and an additional 4 due to his +4 Intelligence modifier. 

So after your wizard has reviewed all his spells in his spell book and selected the spells he wants to prepare he is ready to go.  A wizard would never prepare a single spell more than once.  In 3.5, your wizard might memorize three magic missile spells before adventuring, but in the 5th edition the wizard can prepare magic missile once, but still have the flexibility to cast it zero or many times during the day. 
A 3rd level wizard gets 6 spell slots as shown on the table on page 113.  He gets 4 1st level slots and 2 2nd level slots.  This means that he could cast prepare many different 1st level spells (up to 7), but he could still cast magic missile 6 times, once from each slot.  When a wizard casts a spell, the cast spell essentially fills one of his available spell slots.  And notice that the wizard could cast 6 magic missiles (a 1st level spell) even though he only has 4 1st level spell slots.  That is because you can always use a slot from a higher level to cast a lower level spell, but you can't use lower level slots to cast a higher level spell.  Our 3rd level wizard could cast, at most, 2 2nd level spells before resting.
Some spells, like magic missile, have greater affect when cast from a higher level spell slot.  When casting magic missile from a 1st level spell slot you get three missiles, but when you cast it from a 2nd level spell slot you get four missiles.  When you cast fireball from a 3rd level spell slot you do 8d6 damage, but when you cast it from a 4th level spell slot you do 9d6 damage.  Notice that, unlike the 3.5 edition, fireball damage is not dependent on caster level, only upon the spell slot from which it is cast.
Check out my next post for more changes for wizards.