Heh, well, the main thing about the AI is that it's reactive. It will react to what you do and not the other way around. Yes, there are raiders harassing your borders and triremes landing on your shores but those are rarely serious threats. The AI will almost never launch an overpowering offensive to take one of your cities. Instead it reacts to your moves. Any aggression on your part is met by all the forces it can muster.
And that can be a real problem, hordes of hoplites will put a stop to the best laid plans, but it's also a weakness. The AI is vulnerable to diversions. If you move up a force and draw the AI faction's troops out then it won't be able to stop you from moving a smaller army up to another city and taking it in a quick siege. Spread out your forces, the AI is bad at dealing with attacks on two or three locations at once. One attack might fail but if the others succeed you'll have taken a city which the AI will not try to take back in any serious fashion. Then you just repeat, taking city by city until the AI stops being a threat.
As for more campaign-specific advice the PoM campaign is easier than the others because you have phalanxes and they will beat all hoplites in combat, meaning that as long as you bring enough phalanxes you will almost always win. Almost because if you let enemy peltasts get involved then the odds start turning against you. But that is what cavalry is for. Let the horsemen deal with the peltasts and your phalanxes will handle everything else. The early stages of the campaign are when the raids hit hardest so it's good to keep a small mobile reaction force ready. One or two phalanxes, a peltast, and maybe a scout cavalry unit should do it as long as you try to fight the enemy in range of your city artillery.
The Archidemian War is really hard because your troops are outclassed and you're heavily outnumbered. If the AI actually attacked you the campaign would be over in half an hour or less. To win first beat up any isolated cities you can find to strengthen your economy and then make good use of misdirection to assault multiple cities. You should have plenty of triremes and the AI can't adequately guard every coastal city.
The Ionian war gives you crack Spartan hoplites but they're really slow to reinforce, but since this is an island-hopping campaign the enemy will rarely reinforce the defenders, meaning that if you have enough troops to defeat the city garrison then the city will fall. And with your Spartans the enemy won't be able to beat you in the field. Just make sure to not get your troops caught in transit by roving athenian raiding fleets and show a bit of patience.