I would like to be able to change my webpage background image according to the screen resolution the user uses so:
if screen resolution is greater than or equal to 1200*600 then background = mybackground.jpg no-repeat or else. How can I do this?
Pure CSS approaches that work very well are discussed here. Two techniques are examined in particular and I personally prefer the second as it not CSS3 dependent, which suits my own needs better.
If most/all of your traffic has a CSS3 capable browser, the first method is quicker and cleaner to implement (copy/pasted by Mr. Zoidberg in another answer here for convenience, though I'd visit the source for further background on why it works).
An alternative method to CSS is to use the JavaScript library jQuery to detect resolution changes and adjust the image size accordingly. This article covers the jQuery technique and provides a live demo.
Supersized is a dedicated JavaScript library designed for static full screen images as well as full sized slideshows.
A good tip for full-screen images is to scale them with a correct ratio beforehand. I normally aim for a size of 1500x1000 when using supersized.js or 1680x1050 for other methods, setting the jpg quality for photographs to between 60-80% resulting in a file size in the region of 100kb or less if possible without compromising quality too much.