Page fifteen of the rulebook:

"A stunned investigator only receives one Movement Step during his turn."

Now, does this mean that the stunned investigator only gets one of his two Movement Steps - still being able to take an Action Step - or that he gets only one Movement Step, with no other Steps - neither Movement nor Action?

It means he only gets one of his two movement steps, and has no effect on his ability to perform an Action.

Ah, that would explain why the investigators died so horribly in my first game last night. We were unsure which way it was to be read, and assumed that since monsters couldn't attack while stunned, neither could puny humans. This way, the poor investigators will be able to fight back!