@Cody, in Vanilla, other than laying down your cities in concentric rings you're doing all you can. If you're unsure of how to count the distance from the capitol there are tools that will do this for you.
Build courthouses in cities w/ less than ~85% corruption/waste. If you have a city that's beyond that level of waste then the courthouse will have about zero effect and the time/money spent on building it would have been better off cranking out workers or set to cash. I would go for workers and then set those cities to producing settlers or arty units.
Also on Vanilla, the shared corruption in Communism can be brutal.
Another way to "reduce" corruption is crank up the uncorruptable food production and then use your citizen's lives for 20 shields a pop.
The FP in Vanilla is quite useful in reducing corruption in that city and the surrounding cities. However, you need to build 10+ (probably more like 15) clicks from the capitol to make it really valuable. And to do this that far away takes a long time. Try and cultivate a GL just for this purpose.
In C3C there are more ways to combat corruption that have been noted below. Also, the benfits/need of building your empire in nice concentric rings has been removed
and the FP placement is less important.
FP reduces corruption in that city and does not effectively create another "ring". So building in a far-away city makes an otherwise corrupt city very productive but the benefits of taking the time to do this are offset by the collective reduction in corruption due to increasing your OCN far earlier in a city nearer the core.