Insect reproduction is usually, but not universally, by means of sexual reproduction and the larvae usually come out of eggs that the mother lays on or near a source of food. Some insects can reproduce asexually, and some have both sexual and asexual options.
The lifecycle of insects usually completes in a single year, but many species have shorter periods if the circumstances are favorable, especially in the tropics. On the other end of the spectrum, some cicadas have 17-year life cyles.
The number of eggs is usually large, from a few tens to many hundreds. Fruit flies can have life cycles as short as 2 weeks and can lay a few hundred eggs, so that given favorable conditions the population can really increase explosively.