Step 1: Disconnect the battery
Step 2: Find the leak
First step in finding a leak is to get under the car and follow the bright green coolant trail. Unfortunately, in this case the trail quickly hid behind a pulley.
Second step in finding a leak is to just take everything off that might be in your way off. Don't be timid here; if it looks like it might come off, take it off! I ended up taking off the coolant reservoir, wheel, belt, alternator, idler pulley, water pump pulley, etc... And I still didn't find an obvious leak! Though, I did find a suspicious puddle of coolant on the crankshaft pulley.
Step 3: Really find the leak
So, I pressurized the coolant system by running a hose into it. To make a seal between the hose and coolant system, I used an old bicycle inner tube (Anyone who's hung around TimAnderson knows that these are the solution to all of your problems).
The area behind the water pump pulley starting spraying water. My mission was clear: I had to replace the water pump.