Draining tank and cleaning elements is pretty straight forward. Question though, is your water tank electric of gas? If gas no elements to clean, just drain the tank and try to break up all the mineral build up that can't drain through drain plug.
Most manufacturers have recommendations on what steps to follow for this ANNUAL maintenance procedure, check their website. Otherwise there's some good videos out there.
As for a softener, I'd highly recommend one as not only is your water heater getting gummed up by the minerals but so is every other fixture in the house.
I understand how build up could block pipes but I am trying to get a handle on why toggling the kitchen tap can bring the pressure back or why it goes in the first place. Is it a matter of a pressure change pushing the blockage out?
By switching from hot to cold and back you're probably dislodging a chunk or two which will float back up and eventually block the hot water line again and again.
No comment on rates local to you, but since it's Sunday night expect to pay extra $$$. I'd wait till tomorrow morning, if you're not comfortable trying this yourself.