The main thing to wrap your mind around is that this is used to route blocks of IP addresses (Called Subnets or Supranets) instead of individual addresses. To get your feet wet you would want to try using an AS Lookup tool.
BGP is used to cross from a network owned by one company through to a network owned by another company, or a major subdivision of a very large network within the same company. So this would get you to the core router, and would be used between two core routers on two different networks. The core router itself might be running ATM, Frame Relay, OHC, SONET, X.25, X.75, ect, from core router to core router within its own network.