Look on your heater for the maker and the model number, contact the manufacturer and request a manual. They can probably e-mail you one.
Draining, or bleeding, the heater should be easy. There is a spigot at the bottom, put a bowl under it, open the spigot and keep the water running until it is clear. Depending on how often you do this (we do it 3-4 times a year) it should take no more than 10 minutes and you will lose about a gallon of water. You don't need to empty the whole thing!
You might want to contact your local utility company and ask if they offer a free energy audit. An energy audit will tell you where your major savings will be. For example, just turning off all appliances that have built-in clocks, lights, etc. when they are not in use can save up to 8% on your electric bill.

A hot water heater generally isn't that hard to flush. If you are mildly handy, it is a DIY job. The most difficult part is turning off the heater (shut off gas or electric.) Running heater without water in it can cause damage.

After that, shut off the water to the heater. Then, open up a hot faucet in the house and let the pressure escape. If you have the time, just let it sit for a few hours and cool down a bit. That will keep you from accidentally scalding yourself. The tank will have a drain. You can use a bowl or bucket, but it is easier to just hook it up to a hose and run that outside. Open up the drain and let ALL of the water out. Then, turn the water to the tank back on and fill it about half way up. Then drain the tank again. Repeat until the water runs clear. If you haven't done this in years, there could be a lot of junk built up. Draining it completely and then adding more water helps stir up anything on the bottom.

Once you are done, refill the tank then turn the power/gas back on.

Cleaning out the tank will help it heat water better. It will not dramatically reduce your gas bill though. You might save a couple percent. The real savings come from the heater itself. Letting junk build up in the tank will shorten the life of the appliance.

I'd even say you don't have to be all that handy. Are you able to turn the thermostat down or off? I'm sure you can. Can you use a garden hose? It makes things easier but not required. I wouldn't even worry about turning off the pilot light, just be sure it doesn't turn on, hence, turn the thermostat off. And don't leave it sit with an empty tank for a long time either. Want to ask me how I know? :)

The above instructions are good but you could do it a little simpler if you like. Turn off the supply water to the water heater and hook up the hose or take two or three pails like I usually do, and start draining it into the pails. I usually fill them up, then shut off the water, dump the pails and you'll probably be surprised at the sediment in there. Keep doing this until the sediment is gone is ideal, but if you flush some of it out and come back a week or so later and take some more that's fine too. Once you're at the point where it's fairly clean, then the frequency depends on the amount of sediment in your water. You might try for every 3 months or 6 months but definitely at least once a year.

If you leave the supply water on, it'll kick everything around in there and be much more inefficient at flushing it out.

When I replaced my first water heater it fell apart outside and there was over 2 feet of sediment built up in the bottom of it. That's when I knew the importance of flushing a water heater. My new one however claims to be self flushing. I'm curious about that and the plumber couldn't give me a good enough explanation on it to satisfy me. Anyway, having the sediment in there makes it more difficult to heat the water, limits the amount of hot water and if you use quite a bit, obviously will cost you more to heat it so whether it would be noticeable on the bill, I can't say but whether it's worth doing, I'd say definitely yes.

One little thing that will make some people panic, but don't let it worry you. If you've never done this, the drain valve might not shut off all the way when you've drained some stuff out of it. Relax. Just open and close it a few times and it'll work the crud out of there. If it's just dripping a little, leave it sit with a pail under it or the hose attached and come back in a while and try it again. The first time it threw me but there was no problem after it became a regular chore. Just so you don't get too nervous and think you wrecked something. It's not a big deal.

BTW, when you start seeing a lot of rusty water being flushed out and there hasn't been a hydrant cleaning or something, it's time to plan for a replacement. It's a sign the heater is going.

We had rental property for years and my husband never drained one of them or our own home's and it was never was a problem. The valve you have to open is sometime corroded and can't be opened. A lot of people don't realize how much elec is used by refrigerators. A lot of people have a second refrigerator in the garage and that will run up your bill quite a bit. We had one there temporarily and our bill increased so much I called the company to complain.

The valve you have to open is sometime corroded and can't be opened.
This is a perfect example of lack of maintenance! LOL But it's also a reminder on other shut off valves. For your main house line, lines to your washer, even to your toilet. You should be opening them and closing them occasionally to make sure they don't corrode so they're of use if and when you need them. Break a hose on your washer and can't shut off the water to it? Think about it for a minute. Laziness can get you a mess of trouble, or just a mess.

I also read that this really requires a certain level of skill that I don't believe I have so I assume I have to call a plumber. ?

No,all it requires is that you hook up a garden hose to the drain valve and run a few buckets of water out the bottom of the tank until the sludge stops running out.

AND ... check the "sacrificial anode".

Here is a link that might be useful: Checking sacrificial anode