I am trying to make a ‘dropdown’ menu style of which its a div. When a button will be pressed the div will appear at a position exactly underneath it.
Here is an example from google’s translator:

This is a div and its positioned exactly underneath the button, using left and right.
How can you do this without specifying exactly the left and right because I can’t know the screen size of the user. Also this has to be cross browser.
This is what I currently have:
http://jsfiddle.net/pCg9N/
You could do something like this:
Basically now it’s making use of the button’s positioning information so you never have to set it on the div. This should help, but unfortunately cross-browser support isn’t necessarily this simple.
I also changed the CSS around a little in your example to better illustrate what we’re doing, see updated version below for the full thing:
http://jsfiddle.net/pCg9N/15/
Links to relevant jQuery function documentation: