What am I supposed to do if the water heater pressure relief valve won't stop leaking?

Determine the pressure of the system with a hose bibb gauge. Then determine the temp of the hot water with a thermometer at the nearest fixture. Also, do you have a hot water expansion tank? If pressure is under 80 psi, temp is under 140, you most likely will just need to replace the t&p valve. Under no circumstances can you plug the valve. If you don't feel comfy taking this on yourself, I suggest turning the water heater cold supply off until you can get things checked out/valve replaced.

You need to find out whether the valve if faulty, doing it's job or have a bad house pressure reducing valve.

Adding to Dads and Brians posts. We need answers.
1- What's the house PSI? Check it with a hose bib pressure gage. (see image)
2_ Is there a Pressure Reducing Valve installed (see image)
3- Has the water been hotter then normal?
Let me know, Tom