How does Google Local choose the review sites it displays

And how does one go about submitting a review site to be added

[hannamyluv]

Google Local pulls review snippets from several review sites for various companies.

How do these sites get choosen for this?

[Silvery]

These companies have partnership agreements with Google.

I suspect that to be considered, you'd have to have a substantial number of reviews plus some sort of editorial quality guidelines for them to take you seriously.

You'd need to contact their business development people to discuss integrating your stuff with the Google Maps content.