There are a few ways to answer this question, but the most straightforward way is to divide classes into two camps: those that have one spell slot per class and those that have two.
Multi-classing is possible in D&D 5e by taking the appropriate multiclass archetype, such as the arcane Trickster. When you multiclass, you lose all of your spell slots from your original class, but you gain the spell slots from your new class.
For example, a wizard who multiclasses as a rogue would have three spell slots (one from each of her three classes), while a wizard who multiclasses as an arcane trickster would have one spell slot (from the arcane trickster class).
So how many spell slots multiclass provides? This is a little more complicated to answer. If you are taking an arcane Trickster multiclass, for example, then you no longer have any spell slots from your wizard or rogue classes.
However, you do retain all of your spell slots from your cleric and druid classes. So if you wanted to cast a cleric’s healing word using your rogue’s sneak attack dice, you would still be able to do so since sneak attack is still a cleric spell.
Multiclassing provides flexibility in how you use your spells, but it isn’t always easy to find an archetype that works with your desired playstyle. For example, if you want to play an arcane Trickster who focuses on using misdirection and illusions to confound and confuse their opponents, then an arcane trickster archetype would be a good fit for you.
But if you’re more of a traditional caster who wants access to all of the spells available to wizards and clerics, then multiclassing might not be the best option for you.