Categories Menu Example of what I'd like… Help!??

Ok so I managed to get my website looking pretty cool and just how I wanted it then realised it doesnt display properly in IE (grrrr). I have since decided to simply install a new theme, however the problem now is that it means I will lose the menu option I had in my current theme which sadly I have NO IDEA how to replicate again as I have lost the code etc…

Anyhow I took a picture of what I wanted so that it is more visual for you. I simply want to add my categories as a list on my page menu (drop down and accross list names Articles). Someone pointed me to some codex page before but I simply did not understand it and where to input code etc… I am not techy techy
I do however remember that when I did this first time round a year or so ago it was a tiny bit of code and I THINK it went into my functions.php file??? Anyhow if you can help me to achieve having this menu option when I install my new theme then please please tell me how.

I will leave my page as it is (unviewable basically in IE) until I have some answers then I will install the new theme and hope that the code you offer me can achieve this result!

Here is what i am wanting! http://www.mumsbabymagazine.com/images/whatidlike.jpg

Rach