I can only assume that you have an electric water heater since I can't think of any way that this would happen in a gas water heater.
Anyways, as TomG has said, the bottom element is out. It's hard to say why it failed, but one possibility is that it became covered with sediment, overheated, and then failed.
The first step would be to drain your water heater to remove the sediment and to be able to replace the lower element.
- Unplug your water heater.
- Attach a garden hose to the drain at the bottom of the water heater.
- Run the other end of the garden hose outside.
- Open the drain.
This will forcefully drain the water heater, and hopefully the city's water pressure will be able to get a decent amount of the sediment out of the bottom. Depending on how fast the water is flowing, let this continue for 1-5 minutes. Sometimes the drain can be pretty clogged up or the bottom quite full, and the water won't come out very fast, especially when you disconnect the city's water pressure.
- (5) Open a hot water faucet.
- (6) Turn the cold water off. There should be a gate valve right near the water heater to do this with.
This will drain the water heater. The open hot water faucet allows air into the tank to replace the water that is being drained. This prevents a vacuum from forming. It is imperative that the water heater be disconnected (electrically) at this point, as it is a big no-no to allow the heating elements to be exposed to air while in operation. (They will blow up.)
If you have a pump around that can hook up to a garden hose (or a similar pump with some thread adapters), you might want to connect it to the end of the garden hose to speed up this process.
Once the water heater is drained, close the drain valve and remove the bottom element. Take the cover plate off, take some pictures of the wiring to make sure you know later where things are supposed to go, and then remove the element. If you have a wet vac, attach a hose in there to suck out the remaining sediment. If it gets too thick, open the gate valve up top for 5 seconds to let more water in.
At this point, you can do it yourself or call a plumber (by this, I of course mean that you should call them, schedule an appointment, and do the stuff listed above 2 hours before they came.)
Put a new element in and wire it up. See this video: http://www.youtube.com/watch?v=pNntz_NVLfU .
Before refilling the water heater, you should check your anode rod. This will be a hex-shaped bolt head at the top, sometimes hidden underneath insulation. Undo the hex bolt, which will take a lot of effort. You'll need a socket and a breaker bar, as they are often incredibly difficult to remove. Once loosened, pull it up and inspect it. If it is down to a thin wire or nearly there (see this diagram: http://www.rvingoutpost.com/library/AnodeRodPic.jpg ), you need a new one. If there is a ceiling above the water heater, you'll have to pull it up, cut it with a hacksaw, pull it up more, cut again, repeating this process until it's removed. Just don't drop it back in the tank after you've cut the bolt head off. If you have ample clearance above the water heater, you can replace it with a solid, continuous anode rod, but if there's a ceiling, then they make flexible/sectioned ones like this: http://www.accentshopping.com/ImageGen.ashx?IMG_ID=24592 . Put some pipe dope or PTFE tape on the threads of the bolt head before putting it back in.
Now it's time to fill the water heater back up. Make sure the drain is close once again, and remove the garden hose. Close the hot water faucets and open up a shower faucet instead (the faucet, not the head,) making sure that it's set on 100% hot water. (A shower faucet is preferable to a sink faucet, as they do not have a aerator/screen that any of the stirred-up gunk can clog.) Once the water heater is full of water, you can plug it back in and turn off the shower faucet.