Data centers get internet and network connections from familiar, and unfamiliar (to the home user) providers. Depending on what the data centers serves, different providers and types of circuits would be ordered.
A data center I worked in had circuits coming in from Windstream/Paetec, Verizon, Level 3, ATT, and others. Different providers were used based on different customer needs. Some circuits were used for failover, in case your primary went down, you still had a connection to the outside world.
If you are simply running an internet facing LAMP or FTP server, all you need is a fat pipe (size depends on bandwidth needs) with a static IP. To get that you'll need to order "business class" in most locations, due to ISP restrictions.