To automate fleet, select it and hit 'a' on your keyboard [:)]
There is a level of autonomy, but it seems very context-specific. E.g. If an enemy ship attacks one of your fleet ships (and that ship is in the vicinity of the rest of it's fleet) ONLY that individual will retaliate. Ships are always set to "return fire when fired upon".
That last one I'm not sure on... I think they'll do their own thing until you order an entire fleet command.
I have found that ships in fleets need to be microed a bit sometimes... they will kill their target and sit there taking potshots until they are all dead... if you aren't watching them.
I find it useful to leave fleets on manual then set to "suggest" Attack Targets. The AI does a decent job of suggesting valuable targets during war, like a resupply outfit, or other enemy fleets. However, always leave at least one large fleet to patrol your capitol.