Dumb Question: How to enter in private giveaways?

It doesn't require a password, you simply need to be given the link. Getting the link depends on the people hosting it. Some people come from other forums and will say, post the link on that other forum, or a Steam Group might host one, some are done on this forum, etc.

there's a reason they're called private, you know...

As I understand, giveaway links (currently) have a format of http://www.steamgifts.com/giveaway/XXXXX/name-of-the-giveaway-game where XXXXX is a sequence of 5 letters or digits. To enter the giveaway you only need this sequence (i.e. link http://www.steamgifts.com/giveaway/XXXXX). Hope this helps.