You take note of the time on a clock, you start to write, once an hour has passed, you stop writing.
At which point you should have a complete story.
Beta-reading and editing aren't part of the writing process, if you're talking about correcting the odd typo here and there, so don't count in the hour. Unless you end up doing huge swathes of re-drafting after the story is edited, in which case you failed the challenge.
LabRat