How do you get a divorce when you live in separate states?

Depends on a couple of things.  For instance, where the property and children reside.  But, at the very least, you need to live in a state for a certain amount of time before the court can have jurisdiction.  In short, check to see how long you have to live in your state before you can file.  Then you just file a normal divorce petition and have the other spouse served.

Hope this helps.