Relationship between GIT and coarse moduli spaces

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I'm trying to understand how a generic algebraic geometer constructs coarse moduli spaces. I'm familiar with the definition, and how it is usually quite involved to show that a space has the coarse moduli property. It seems that Mumfords GIT takes care of this somehow, although it seems to me that GIT is a way to construct 'nice' quotients. How does this interact with the moduli property?