A leaking hot water heater tank is generally a death knell for your water heater. Once the tank goes bad there is little you can do. However, water heater tanks do last a long time, so you want to make sure that it is not something else before you assume that the tank is bad.
Water Leaking Onto the Floor
Just because you see water on the floor does not mean that your tank is leaking. It could be leaks from other spots on the water heater that are less costly to fix.
Is the water leaking at the base of the tank? Look inside the metal casing below the tank. Do you see water? Is the water persistent? Have you checked the other fittings on the tank?
Water Heater Drain Valves
The water heater drain valve is near the bottom of the hot water tank. They can and do start to leak. A bad enough leak at this location can puddle up on the floor and make you think the tank is leaking.
See the article 'Leaking Water Heater Drain Valves' for information and instructions on what to do with this component.
Pressure Relief Valves
The temperature and pressure relief valve is located near the top of the hot water tank. However, it has an extension pipe that directs the water toward the floor. Sometimes this is routed to a drain.
If the relief valve vents water it will wind up on the floor. Although this is a problem, it is not as serious a problem as a leaking water tank. See the article, 'Checking a Water Heater Pressure Relief Valve' for instructions to rule out this possibility.
Condensation is a somewhat rare occurance that would only happen when the tank is filled with cold water. When you start up a water heater that is new or has been worked on, it is filled with cold water. When you start it up, the tank will get some condensation on it that will drip down onto the floor.
Make sure it is not condensation, see the article 'Water Heater Condensation' for more information. The tank is likely corroded or cracked. Your really do have a leaking hot water heater.
Other Leak Locations
The hot water heater has a cold water supply line and a hot water outlet line that are filled with pressurized water. Leaks from the water line may be an issue.
See the article on 'Leaking Hot Water Heater Pipes' for information on what to look for and how to correct this problem.
Vent Back Draft
Gas water heaters have vents at the top. A vent that is back drafting can cause condensation on the top of the hot water heater. See the article 'Checking Water Heater Vent Draft' for information and what to look for.
A chronic leak at the floor, that cannot be explained any other way probably means that the tank is leaking.
Unfortunately, you cannot repair the tank. The water heater will need to be replaced. How long to you have before it lets go completely? Great question, but there is no good answer. You may get away with mopping up the water for a while until you can replace it. Or, worst case scenario, it could let go immediately and you will have a big mess on your hands.
Changing the water heater is a big job. Depending on he location of the hot water heater the age of the plumbing and your own skill level you may not want to tackle this job.