AI won't war against his friends (his real friends anyway, but sometimes you can detect that they are being deceptive toward another AI).
An AI you are not on good terms with will not war with anyone but its enemies (so, if the AI was just warring with a neighbor, then for some reason made a peace treaty, you can pretty easily pay the AI to get back into that war after the mandatory 10-turn peace ends).
Improving an AI's disposition toward you by gifting, denouncing someone he's denounced, friending someone he's friended, sharing embassies, etc, will help lower the price (like with all other types of trading).
AIs with huge standing armies are more easily convinced to use them (assuming they are not already in a war) somewhere, anywhere. It is usually instructive when your spy learns that X is plotting against someone. That means that civ is ready for war, and you can usually convince him to pick a different target if you want. This is pretty clutch. Assuming you do not have a huge tech edge (in which case, stick him in your capital!), and you are playing a style where diplomacy matters somewhat (basically anything besides super-warmonger or complete isolation), it's a pretty good idea to send that first spy hopping across everyone's capitals. He'll never get caught, and he'll catch all the intel, which you can then selectively share and make better allies, while helping them defend themselves at the same time.
Also, some AIs can be more easily convinced due to their personality. These are usually pretty obvious (Atilla, Genghis, Monty, etc).
Remember that for the most part, the AI is pretty good about only going to war when it has the advantage, so between two AIs, most of the time, the AI you told to go on the agressive will win out (and become more powerful in the process).
