There is a lot of confusion regarding how to calculate the number of spell slots you get when you multiclass. This is my attempt at explaining it.
Spells Known and Prepared:
You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.
Pact Magic is what gives a Warlock the ability to cast spells. Warlocks on their own do not gain as many spell slots as other D&D 5e classes, such as Wizards or Bards. However, a Pact Magic allows them to regain all of their expended spell slots upon finishing a short or long rest. A multiclassed 1st level warlock / 1st level wizard would have a total of three 1st level spell slots (two from the Spellcasting feat and one from the Pact Magic feature), all of which can be used to cast a 1st level spell from either the warlock class or the wizard class.
Spell Slots from the “Spellcasting” class feature:
• Add together all your levels in the bard, cleric, druid, sorcerer, and wizard classes;
• If you have one or more levels in the artificer class, add half these levels (rounded up);
• If you have two or more levels in the paladin class, add half these levels (rounded down);
• If you have two or more levels in the ranger class, add half these levels (rounded down);
• If you have three or more levels in the fighter (eldritch knight) class, add one third these levels (rounded down);
• If you have three or more levels in the rogue (arcane trickster) class, add one third these levels (rounded down);
Use this total to determine your spell slots by consulting the “Multiclass Spellcaster: Spell Slots Per Spell Level” table (PHB p. 165).
Spell Slots Dnd
Note regarding Warlocks:
Warlocks do not have the “Spellcasting” class feature. Their spells come from the “Pact Magic” class feature. You track warlock spell slots separately from any class with the “spellcasting” class feature. However, you can cast any spell that is available for you to cast form any class using any spell slot of the appropriate level on your list of available warlock spell slots.