First of all, you have to have a background in requirements engineering. As a start, look at the Volere templates, that help to organize the requirements in a meaningful way (http://www.volere.co.uk/templates.htm). The authors (the Robertsons) have written a book "Mastering the Requirements Process" (ISBN: 978-0321419491), but there are of course a lot of other authors.
There are a lot of techniques to get requirements from the customer, and it depends on how the customer behaves, in which area he is under way, and how much experiences he has there. It is not possible to give here any advice.
I don't think that there is a list of common mistakes that could help you in any way. Get an experienced requirements engineer, and follow his steps.