Check out Martin Berkhan's http://leangains.com for more about making muscle gains while fasting. There's a subtle difference between using fasting as a tool for weight loss and one for body fat loss, but it's a difference nonetheless—it largely boils down to better management of your macro-nutrients (proteins, fats, carbohydrates) versus "eating like normal" after a fasting period.

The most basic explanation is that you can fast whichever periods you would like (most do 16 hour fasts + 8 hour "feeding windows"), but you must:

  A) Lift weights no more than 3 days a week
  B) Lift heavy weights to stimulate muscle growth
  C) Eat more carbs / less fats on workout days (more calories)
  D) Eat more fats / less carbs on "rest" days (less calories)

Compared to most lifestyles (this isn't a diet) this takes a lot of mental preparation and calculation, so it is more daunting initially and less mentally draining as you go on and see results (as compared to a fad diet which is simple to implement but impossible to maintain). It's not easy but, once a routine is established and the learning curve is overcome, many people make the decision to keep the 'LeanGains' lifestyle for the remainder of their lives.