Remembering If A Div Is Open Or Closed?

The first thing I'd like to do is show/hide divs. What I'm going to do is pull out a few bits of PHP code out of the database and assign them all a class of show or hide. So, I need a script that can either open or close a div using a link using classes, probably with AJAX or DOM? The main thing is that it needs to be compatible with all major browsers. I've scoured the internet but can't find the most simple of scripts, and unfortunately my AJAX/DOM is terrible!

The second thing I need to do is remember which divs are open or closed. I was thinking of doing this with a database, and so I'll need to run a tiny PHP script to update the DB whenever a div is opened or closed. I assume this would be done using an onclick event? If so, I probably need to use GET to update the new class in the DB. Any ideas how I'd work out whether the div was open or not, and what function I'd use to run the PHP script?

Also, every time a page is loaded I'll get the 'show' or 'hide' options from the DB and assign them to the classes so the user still has their preferred tabs open.