Question

How do mushrooms multiply?

Answer 1

The hyphae gives rise  to  new fruiting bodies, the fleshy, capped structures  that produce spores and are harvested  as crops.

Answer 2

Mushrooms are a type of Fungus, really. Now, mushrooms, like anything else, reproduce sexually, but also Asexually. 

Sexually: Two different mating types fuse before forming a new fruiting body, which is actually what we call the "Mushroom", the above-ground part of the fungi that is visible. 

Asexually: Can happen two different ways. Both are complicated, so I'll save you the explanation. Either spores are released into the air, or separation, in which each separate mushroom grows individually. 
The environment the mushrooms are in can trigger any one of these.

~Hope this helps!