Cleaning real hard-wood floors....

Ok, so what is the best, most frugal way to clean hard wood floors? I have a regualr swiffer and a wet swiffer. I know I can use the regualr swiffer to dust it... but I am moving in to a house where its all real hard wood floors and the lady had 2 cats. Not sure if I can use the wet swiffer and don't want to do anything to damage them... The kids and I are allergic to cats so I need to clean the floors WELL before we move in. What to use? Thanks!