How quicklyor slowly do igneous rocks form under the earth's surface?

Answer 1

Geolicious' answer is quite correct, but in addition to depth, pressure, and time affect the formation of igneous rocks, as does the chemical constituency of the magma.

Literally speaking, at the mouth of a volcano, the lava being ejected is not rock, but liquid. The rock forms as the lava cools. The lava still in the volcano will also cool as the pressure decreases, and various kinds of igneous minerals will separate out of the super hot liquid. How quickly all this happens is a function of pressure, depth, chemical (elemental and mineral) constituency and time.

Answer 2

Depend upon the depth. The deeper the magma is the slower it will cool (providing it is a depth that will allow cooling at all). The slower it cools the larger the grain size and texture. Intrusive magmas are a slowly cooling substance.