In a nutshell, it is every Friday (except Christmas Day), Saturday and Sunday night starting the Friday after Thanksgiving and running through the Sunday following Christmas, 5 p.m. - 9 p.m. (14 nights total). Weather permitting - if the weather is questionable, check Kennywood's Facebook page to see if there is a cancellation (they usually make the call by 2-3 p.m.) or call the park. They usually only cancel if there is heavy rain or if there are icy conditions on the midway and in the parking lots or if there is more snow than they can remove or salt away.
Best single-day admission price tickets are at participating Giant Eagles, but for those that can go more than once, the season passes are the best value.
Here is the direct link to the pages with all of the details.
Andy