*chuckles*
You always seem to end up on an island too, huh?
From my experience, the best strategy for an island civ is to emulate history. Think about it, those civilizations who stayed on their island and were quite happy with what they got were either conquered or "colonized". That's with every civilization that didn't expand. Take the Aztecs for instance. They focused on culture and economy rather then science and warfare and stayed put. It only took a seafaring civilization such as the Spanish to land on their shores and walk in to their cities.
So when you start on an island by yourself:
The best thing you can do is build good defenses so nobody can conquer it.
Build colonizisation fleets and explore the world for other shores.
When you find another land (be it a uninhabited island or a empty part of a continent) build colonies that will eventually be able to support and defend themselves.
Focus on science. Hopefully no other civ will bother you and your island for at least the stone age. If you can use this to your advantage and let your cities florish with culture then you may gain an advantage over the other civs.
Build a navy! This navy should be split into two groups. The exploration navy bent of discovering every part of the world and the defence navy. Often navies are underused. If you can tactifully deploy a dozen military ships around your island you can create a very effective wall against enemy landings. They won't even be able to reach your island!
It's always fun trying to control the seas. So what if you are stuck on a island and have not much room to excerise your soldiers? If you can control the oceans or at least the major shipping lanes it will cripple the other civs. It's very hard so don't overextend yourself.
If one of your exploration navy ships chance upon a civ you haven't met before.. assess that civ. Is it a mighty civ with great culture or is it just a bunch of natives? If you are technology and militarly superior it might be a good idea to conquer them and take their land. Or maybe they are quite a rich and cultured civ with many big cities. Then you might just open trade routes with them. That way you reap constant money/science and don't have to have anymore contact with them. You might want to check out their techs though. To make sure they aren't capable of overrunning your defence navy and conquering you!
General rule of the thumb:
If you start on a island you are bound to be conquered by some mighty empire unless you do what the British did and create mighty colonies to support your civilization!
So, to wrap up.. If you are on an island it can be as fun as when you are on a large landmass with many other civs. You just gotta play it right
