Step 1 is to figure out where the water is coming from. A couple months ago, the relief valve on our 12-year-old water heater failed. It cost me all of $15 for the part (available at your local hardware store), and less than an hour to replace, including draining the tank and refilling it and bleeding out the system.
If the tank on the water heater is rusted, then yeah, it needs to be replaced. At its age, it's to be expected. I'm assuming the water heaters are hooked up in parallel, since that seems to be the most common approach. If you want to isolate it, you'll need to close off two valves, one on the inlet and one on the outlet. Also, unplug it and turn off the gas to it. On valves, perpendicular means shut off.
On your remaining, non-leaking tank, you'll want to replace the anode ASAP. Water heaters basically last until the sacrificial anode is completely consumed, after which the tank will start to rust. Most people don't realize that the anode can be cheaply replaced, thus extending the life of the water heater greatly. I just did that as well, and it cost me $35 including shipping. It sure beat having to pay $900 for a replacement forced-draft water heater, plus hours more installing it (or hundreds of dollars to pay a plumber). I've attached a picture of our old anode next to its replacement.
Also, your water heater should get flushed annually, to get rid of scale buildup inside the tank.