In a plumbing emergency, it is vital to act quickly and to keep calm. That can minimize the amount of damage your property sustains. First, you need to do some detective work. You need to figure out where the water is coming from. Is it a pipe that's leaking, or is it a bathroom or kitchen fixture? If it is safe, turn off your main water valve. That stops the flow of water and gives you a little time to make repairs. Main shut-off valves are usually located very close to the water meter, which is often found in a basement or utility area.
After you have stopped the water flow, you should assess the damage, but do so cautiously. You want to avoid putting yourself in any kind of danger.
Look for signs of severe water damage. You know your house, and you should be able to fairly quickly identify areas that have taken on a lot of water and are in danger of more serious damage occurring. Pay attention to what should be hard and dry versus what is now soft and yielding under pressure.
Look up and look down. Check your walls, ceilings, and the floors beneath your feet. Take special note of any plumbing fixtures that seem to be more dysfunctional than usual. If there's any pooling of water going on, make sure you find out where it's coming from and stop that source. And if you can, take pictures. You'll want to document this for when you get a professional or talk to your insurance company.
Your following step should be to get in touch with a licensed plumbing professional. When you do, state your predicament so that it's perfectly clear, and give them all the details about what you've already done and how extensive the damage seems to be. A good plumber can and will walk you through any emergency safety steps you might need to take to secure your situation until they can actually get there and help you more directly. In my case, I seem to have an extensive plumbing emergency mostly because I don't seem to know much about plumbing in general.