As the only superpower, I try to appease the other civs so they don't gang up on me. I'll give out little gifts of money, and when I get far enough ahead in tech I'll sell a few back to all the civs at once to make some more cash.
Ideally, you want the other civs to fight amongst themselvesx, but that can be difficult to do unless you know some civs are angry and you start giving one some resources to make better units.
With one or two close opponents and the rest far behind, I tend to hunker in my bunker and try to get ahead on tech. The key is not to accept any MPP's that can drag you into a war you don't want to fight. I'll also usually give more help to the minor civs in hope they can be more of a thorn in my opponents side.
However, this backfired on me in a recent game when I was focused on the Egyptians as the threat, and the Japanese came up and became the number two civ, threatening my position.
I think the superpower position is great, as it means you have the biggest/best infrastructure, so you can grow faster and get tech faster, as well as being able to quickly build more wonders.
I always avoid giving any strategic resources or techs to the #2 civ, so as not to help them any more than I need to. I'm more liberal with the smaller civs, as even a little civ can be a pain if they decide to throw a bunch of troops your way, and it takes resources away from crushing the #2 civ.
As far as the definition of a superpower, I'd say that if you have at least 40-50% more score/power than any other civ you are well ahead of the game. I've yet to lose a game in which I had a substantial advantage halfway through.
- ICMB