Thats a great quote that I haven't heard before. I like "Success Is The Best Revenge" . I would have took yours to mean if you have been wronged then just be impassive and let the wheels of justice roll out the fair allegations, findings and consequences. I don't think being cruel or harsh comes into it, just be procedural.
I agree with the second part of Cjkenkel's answer. In the contexts that I've heard it before, I get the impression that it means to do it a substantial amount of time after the event occurred. I think the intention of that is to take A LOT more time to think about the best possible way to go about it, for maximum impact. I have generally got the impression that it would be done after a year or more. But I suppose it depends on each situation. I think also if you leave it for a long time, you get to incorporate the 'get you when you least expect it' thing in at the same time. I've personally never bothered to cook up some revenge scheme, but whenever I get the urge, the 'best served cold' idea always comes to mind. I like the thought of maximum impact, over instant gratification.
This is a saying in some great American movies in the last 5 years. Along with what CJ said, it can also mean that to take revenge on someone, you have to make yourself "cold ", meaning unfeeling or without emotion, for if you had the proper feelings, your ability to carry out the revengeful act to your best ability would be harder to do. Serving "it" cold can have the meaning that you would do the revenge without a conscience and walk away from the act without any feeling of remorse... and not lose a wink of sleep over it.
As in when you want to have revenge on someone, you wouldn't do it nicely; that defeats the purpose. Cold as in harsh an mean, that way revenge is worth it. If someone tripped you on purpose, you might want to get them back. You wouldn't do it by buying them a teddy bear, would you? Instead you'd make it cruel, like telling his crush embarrassing things about him that "did" happen.