The article of Richard Hain "Lectures on moduli spaces of elliptic curves", arXiv:0812.1803, is a very good introduction to the subject, wich contains a lot of motivations. Here you can learn many things about orbifolds, and there is also an appendix on stacks.

The article of Richard Hain "Lectures on moduli spaces of elliptic curves", arXiv:0812.1803, is a very good introduction to the subject, which contains a lot of motivations. Here you can learn many things about orbifolds, and there is also an appendix on stacks.