I don't play online, but have played many isolated starts.
One of the first things I do is settle a coastal city and get sailing early. Get a trireme out to see just how isolated you are. You will often find that your island is connected to the main continent by shallow water. If not, you can at least build two trade routes (with sailing) to send to city states, or to your own cities for growth.
And you need to prioritize growth. Growth will allow you to tech faster to astronomy, which will allow you to get caravels to explore. That is unless you are Korea, which has to get to Navigation to explore the seas.
Also consider taking 1 point in exploration, for faster ship movement and sight (and the Lourve). Since you can't take over an entire land mass, try to take over the seas. Ships will probably be your main units, since no one can really attack you by conventional means.
Isolated starts lend themselves to Cultural and Science victories, since you are less likely to be hated by everyone.