An example of a couple of typical campaign turns:
Theres a system with 4 unocupied dead worlds (yes its a crap system and not technically possible to generate by the normal rules but its just an example
) Hypothetically, lets call them world 1, world 2, world 3 and world 4. There are 4 players, Narn, Minbari, EA and Centauri who roll initiative and end up in that order.
First the Narn player chooses to attack world 1. The minbari player has the option to intercept him, he passes, the EA player then has the option to intercept him and chooses to, the Centauri dont get the option to intercept because the EA player has already chosen to. The EA and Narn player will fight a battle with the winner gaining that target.
Now the Minbari player gets to pick a target, he chooses to attack world. The Narn dont get a chance to intercept as they are already attacking a target. The EA player doesnt get a chance to intercept as he is already intercepting another target. The Centauri now get the chance to intercept but choose not to.
The EA player would now get to pick a target but cant since hes already intercepting another attack with his move. So the Centauri now get to pick a target. They cant pick world 1 or 2 since both have already been target by other players (and they chose not to intercept world 2 when they had the option) so they attack world 3. Since all other players are already attacking a target or intercepting noone can oppose this. (It should be noted that whilst it might seem from this example to be an advantage to go last in the first campaign turn but bear in mind in a proper system the all the good targets will get attacked first so if you go last, whilst noone will be able to stop you, the target you take unopposed will most likely be a big pile of arse....)
Everything is now resolved, lets say the Narn player wins the battle so the Narns take world 1, the Minbari take world 2, and the Centauri take world 3. World 4 is still unocupied.
Now we come to turn 2.
For the sake of simplicity lets assume they roll the same initiative
First off the Narn choose to attack the remaining unocupied target. The Minbari pass on intercepting, as do the EA, but the Cenatauri are determined to deny the narns an early lead and choose to intercept.
The Minbari then get to choose a target. They cant attack worlds 2 or 4 (since they own 2 and chose not to intercept the attack on 4) so they decide to attack World 1 since the narn will already have some of their forces commited to attacking world 4. Since the target is alreayd owned and has a defender there is no option to intercept.
The EA player now chooses to attack the Minbari held world 2.
The Centauri do not get to choose a target this turn since they are already intercepting the narn attack on world 4.
In the end phase the Narns must fight 2 battles, 1 to contest world 4 and one to defend world 1.
The Minbari must fight 2 battles, 1 to attack world 1 and one to defend world 2.
The EA only fight one battle to attack world 2.
The Centauri only fight one battle to contest world 4.
.....I can go on if anyone is still not clear on how it works but I think that would all be pretty clear now!