What tools are required to replace a spoke?
A spoke wrench is required, the stand and tension meter are optional but can make your job easier. You can use the frame of your bike and the brakes if you have rim brakes as your truing stand. If you have disc brakes you can use wire/zip ties wrapped around your frame tubes and poking toward the rim then trimmed to measure true (assuming the wheel is aligned in the frame.)

If you are replacing a spoke on a rear wheel you will likely need a lock ring remover and chain whip to remove the rear cassette.

Note that each time you break a spoke, the others become a little more fatigued, and a little more likely to break. Over time you may find yourself breaking spokes with more frequency. My rule of thumb is that if I've broken 5 spokes on a wheel I get it rebuilt, or at the very least professionally trued and tensioned.

Like most things the late Sheldon Brown is a great resource as is http://www.parktool.com/blog/repair-help/wheel-and-rim-truing.