[JoshTriplett]

You would need to sign up with one or more of the major transit providers, such as Cogent, HE.net, Level 3, XO, or similar. (Or someone who resells such service.) You'd obtain an agreement to hook up that fiber to the Internet (such as via a https://en.wikipedia.org/wiki/Meet-me_room that the fiber leads to), and pay for the amount of transit you use (commonly billed either by the actual amount of traffic or by the 95th percentile of bandwidth usage). Then you'd need all the necessary equipment to get that connectivity to the various customers. And you'd need either a block of IP addresses to hand out or a NAT infrastructure.

(That leaves out all the non-connectivity-related issues you'd also have to handle, such as billing, cutting off service, collections, abuse reports, legal notices/investigations, support requests, etc.)