Leaky drain valve

Under the gas valve is a removable panel. On models of that era there should also be a second panel behind the first. remove both.

the pilot light should be clearly visible.

If no pilot, turn the gas valve to OFF. wait 60 seconds. locate the tubes from the gas valve to the pilot location. turn the valve to pilot, and with a long match or grill lighter lit, place flame at the pilot location and press down on the pilot button beside the main valve.

pilot should light. If not shut off the gas and call a technician. If yes, hold the pilot button for 60 seconds, then slowly release. Pilot should stay lit. If not, shut off gas and replace thermocouple, start relight sequence over. If pilot stays lit, replace inner cover and adjust temp to 120 deg. If heater fires up, replace outer cover. Done.

If heater does not light, replace gas valve or entire unit. Water heaters have a limited life expectancy, and if my recollection is correct your unit is 10yrs past warranty.

What brand, model, and approximately how old is water heater?
This is important because water heater designs are changing quickly.
Did you remove door over combustion chamber to access thermocouple?
Newer Rheem water heaters have air intake under combustion chamber that has to be blown out using compressed air.
If this is different brand, then use mirror under water heater to see air intake.
Set water heater on bricks to avoid high water. Make sure drain line out of drip pan is 3/4" and terminates in good drainage location.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html

Put brass garden hose cap over drain valve.
http://waterheatertimer.org/How-to-replace-water-heater-drain-valve.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

1) Get more air to the water heater and see if problem continues.
2) Read the following pdf-s for things that might apply to your situation.
http://waterheatertimer.org/images/Negative-pressure.jpg
http://waterheatertimer.org/pdf/Attic-Ventilation-and-Pilot-Outage-in-Gas%20Water-Heaters.pdf
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf

3) Read pdfs above first, and then Add a comment with missing information below, for possible do-it-yourself help.
Does this water heater have a blower?
Is gas valve electronic? Or does gas valve have a dial?
If gas valve is electronic, have you checked outlet with circuit analyzer?
Did pilot light work correctly for a while? If so how long?
Where is water heater located? Hot attic? Closet? Garage? Is area dirty and dusty? Has air intake been cleaned?
What color is pilot flame? Clear blue or yellow-or-orange?
Have you inspected inside of combustion chamber for dripping water?

If pilot lights and flame is robust and clear blue, and pilot goes out later, then some suspects can be excluded: air in gas line, low gas pressure, thermocouple is overtightened (finger-tight + 1/4 turn), thermocouple not positioned correctly in the flame, dirty pilot tube.
If flame is yellowish and small: then clean pilot tube and combustion parts.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#clean
Remaining suspects can include: air in gas line, low gas pressure, bad gas control valve, tight house so household vent fans pull air down water heater vent that blows out pilot, hot attic with inadequate ventilation, water dripping down vent.

Open following links to read troubleshoot resources.
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

If you mean the drain valve, then buy garden hose cap at home center.
Cap will have rubber washer that seals tank.
If drain valve is plastic, the cap may not thread on without sanding down end of plastic drain valve.
Otherwise replace drain valve, which is simple if drain valve is brass, but can be difficult if drain valve is plastic.
Turn off power to water heater: Electric: turn off circuit breaker. Gas: turn knob to pilot.
Turn off water, open bathtub spigot on Hot side, drain water heater, remove drain valve with wrench.
If plastic drain valve breaks while being removed, then 'gently' break out broken part using hammer and big screwdriver.
Buy new drain valve at box store in water heater department.
Put teflon tape on new drain valve threads.
http://waterheatertimer.org/Water-heater-is-leaking.html
http://waterheatertimer.org/Water-heater-will-not-drain.html
http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html

Add a comment for more free help.
Also take advantage of fixya expert assistance live.
For a price, expert works with you while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

If you have a leaking water heater there is a serious problem.
http://waterheatertimer.org/Water-heater-leaking.html
Page shows how to limp along on a leaking water heater if your water heater needs replacement.

One of three things is causing the water:
1) Loose water connection on top of tank that is dripping down inside tank >> check pipes on top of tank.

2) The vent is clogged or not working correctly causing condensation inside flue pipe.
Condensation water is dripping back down inside tank.
Problem means possible CO poisoning if gas is not venting.
Look at vent pipe to see if joints are corroded.
Use long fireplace match > light match and put into draft hood at top of tank and see if smoke goes up.
Put hand at draft hood opening when water heater turns on to see if vent gas enters home.
Do same test when furnace turns on to see if furnace vent is pushing back into water heater.
Does water heater vent inside same pipe as furnace? You may need to set up separate vent for water heater if furnace gasses are pushing back into home.
Check furnace vent for obstructions.
Look at vent stack top of home to see if hood is in place.
Check if bird nest is built inside warm vent pipe.
Improper flue is top priority for getting fixed so vent gasses properly escape home.
You may have to call a plumber.
Professional plumbing forum:
http://www.thetankatwaterheaterrescue.com/forums/forum3/

3) Your water heater is rusted out.
A rusted tank has to be replaced.
It cannot be repaired.
However, before replacing tank, you do not want a tank failure where tank ruptures and water runs inside home until water is shut off.
This will cause major damage.
Protect yourself first.
Turn off water valve above tank.
Move gas knob to 'pilot' so burner is not heating water.
Open tub spout on hot side to relieve pressure on tank so it will not rupture.

Now you're protected.
Link above shows how to limp along on failed tank until you can replace heater.

You need a new gas water heater from Lowes or Home Depot
Look at label on side of you tank for gallons and btu's of your water heater.
Measure height to flue pipe so you get same height water heater, so pipes don't have to be changed.
You need a pipe wrench and teflon tape which will be wrapped on each pipe thread when pipes are reassembled.

Step1) Drain water heater using valve at bottom of tank.
http://waterheatertimer.org/Water-heater-will-not-drain.html

2) Turn off gas valve going into heater.
When gas valve is perpendicular to gas line, then gas is off.
Dissemble gas line to water heater.

3) Disconnect flue pipe and support flue pipe with wire so it doesn't not fall down. Flue pipe joints should be held together at each joint with 3 screws.

4) Turn off water. Shut off valve is on COLD side.
Disconnect water pipes.

5) Move old water heater out of way.

6) Set new water heater in place. Put water heater in drip pan.

7) Connect water pipes >> cold goes to side marked cold.
Hot to hot.
Buy new flexible water connector pipes at home center for easy installation of water pipes.

8) Connect gas line exactly as it was connected before.
Home center sells flexible gas line connector for easy installation of gas line.
To test for gas leak after installation, mix liquid soap with water and put around gas line joints to see if there are bubbles.
Natural gas has less pressure than water lines, so gas pipes are easy to seal with ordinary wrench.

9) install TP pipe that runs to floor. Use old one off old heater.

10) Fill tank completely with water until water is coming out of tub spout.

11) Turn on gas, and light pilot as shown in manual.
New gas heater sometimes have small water leak when first fired up, so ignore a bit of water.

12) Save water heater manual like it is gold, and read everything in manual.

Usual problems are:. Bad thermocouple, Bad vent, blowing pilot outl. Too small of pilot flame. Low gas pressure Leaking water heater, dripping on pilot. Bad gas valve. If your water heater is more than 8 years old and the gas valve is bad, I would replace the water heater. IF you decide to replace the pilot or the gas vavle, be sure to mount pilot exactly as is was designed. If you replace gas valve get an exact replacment or a "listed" replacement. If you'rd doing this and it's older, replace the temperature/relief vavle also. Water heaters can be very dangeroius if not properly repaired/maintained.

Sounds like you have a bad thermostat. You can change the thermostat, but if the heater is more than 8 or 10 years old you might be better off to replace the entire heater. Thermostat replacement is easy:
1 turn off the gas 2 drain the heater 3 unscrew pilot, main burner, and thermocouple lines from bottom of thermostat. 4 unhook gas line from thermostat. 5 unscrew thermostat from heater tank. Use pipe sealer when you install new thermostat, and gas line fittings. burner and thermocouple lines seal on a taper seat and do not need sealer. after reassembly check for leaks with soapy water, not a match, light the pilot and turn up the temp. The heater may sweat quite a bit while it is heating up the first time, this is due to the cold water on the inside and the fire on the outside. some water may drip in the bottom of the heater and you might think you have a leak, but let it heat up completly, if the water is still dripping after the tank is hot then you need to find the leak.

IF no gas comes and the piolet is lit then the gas valve is stuck. You can purchase a seperate gas valve and replace it. If it is cost justified ,you will have to determine. As far as I know, one  cannot disassemble and repair the gas valve as you cannot purchase the parts for it.

If you are refering to the "Dripping coming from the preasure tempature valve,Then just turn off the valve where the water goes into the heater and open the P/T valve with a bucket below it draining only emought water to get below the level where it reaches.     Normally the drain valves are plastic with a Male hosebib attached.  Attach a  garden hose to the rain and run it out to a point lower that the vaslve in order for gravity to drain the tank.The valve opens counter clock wise. If the valve is stuck or does not drain,and you have a foor drain handy,remove the whole valve and replace it with a boiler drain valve.  If The tank is located below the drain level then you will have to either pump or carry the drain water to the higher level.     Replace the P/T valve  and reinstall the associated associated piping. I would use tefelon tape on the P/T pipe theads.    You may have to open a hot water faucet in order for the air to replace the water in the tank ,in order to drain.