How do I test the hot water heater relief valve

First, you want to find the relief valve on the hot water heater It is usually located near the top of the hot water heater and you should see an overflow pipe (copper) that goes down the side of the hot water heater connected to it. This pipe is where the water will be directed if the pressure builds up.

Place a bucket under the overflow pipe to catch the hot water when you release the valve.
Carefully lift up the relief valve. This will discharge water from the tank, through the overflow pipe and into your bucket. Only allow the water to flow about 2 seconds and then shut the valve off.

Be careful not to get sprayed with the hot water coming out of the tank.
If no water comes out of the tank or if the flow is not steady, then your relief valve has failed this test. If you notice the valve is leaking or is hard to move, you will need to replace it. If this happens, you will want to remove the tag that is on the valve and take it to the home repair store to purchase a new valve.

You need to get an exact replacement, so ask for help if you aren't sure.
To replace the valve, yourself, you will want to cut the power to the hot water heater off at the breaker box and then turn the water off that is coming into the hot water tank.

You are going to need to drain some of the water out of the tank. If your valve is on the top of the hot water heater, you will only need to drain a small amount. If the valve is on the side of the tank, you will need to make sure the water level is below the valve area (you will need to drain about about 5 gallons).
Once the water level is below the valve, you will want to disconnect the overflow pipe by using a wrench. If your hot water heater does not have an overflow pipe, you will skip this step.

Using a pipe wrench, you will want to unscrew the valve. This might take a bit of strength depending on the condition of your valve and if there are mineral deposits around the valve. If the valve just won't budge, try spraying it with some WD-40.

Once the old valve is removed, you can replace the new valve and then attach the overflow pipe to the new valve.

Make sure you turn the water back on and let the tank fill back up BEFORE you turn the electricity back on to the tank. Give the hot water heater time to heat the water (about 30 minutes) and then test the valve to make sure everything is the way it should be.
Other Resources:

How to Drain Your Hot Water Heater

How to Check Circuit Breakers or Fuses in Your Home

How to Inspect Electrical Cords for Damage

How to Inspect & Replace Electrical Receptacles and Switches