My house is 11 years old and I replaced the hot water tank last September. It's electric.

About 8 weeks ago when I got up, there was no hot water for a shower. I ended up turning the main switch for the tank off and on again and I also did the same in the main circuit breaker box even though it hadn't appeared to trip. The water began to heat.

Then yesterday, the same thing happened and again, was resolved by the same process.

But where do I even begin to trouble shoot what might be causing this?

Here is a trouble shooting video,

https://www.bing.com/videos/search?q=troubleshooting+an+electric+water+heater&FORM=VIRE1#view=detail&mid=984BC82ECD33FF78D63F984BC82ECD33FF78D63F

And as you see an ohmmeter and how to use it is essential.

I ended up turning the main switch for the tank off
What switch are you referring to?

Saw the Video, Made a short story long.
Turn power off to Water Heater, remove both front covers, insulation and plastic covers.
Look for 240 volts at top 2 screws, then basically walk the meter down the terminals, through the thermals then the thermostat and then down to the element. May have to turn thermostat to engage element, Then with a Meter and an Amprobe check to see you have voltage and Current, If you have voltage and no current, the element is open. Dual Elements use one at a time. If a 4500 Watt Water at 240 Volts, then divide 240 into 4500, and that equals 18.75 Amps. Which needs to be on a 30 amp Breaker. A 20 amp Breaker at 80% is 16 amps, That's why the 30 amp breaker on #10's. I feel you may have Either loose wires on the Breaker(s), a Bad Breaker(amprobe will tell)Loose wires can heat up breaker as well as a burnt, dirty, corroded, or burnt buss(what breaker plugs onto) Breaker should be removed to verify clean contact on buss. Good Luck.