How to make a div’s background color translucent?

You can use the background-color: rgba() notation:

#theIdofYourElement,
.classOfElements {
    background-color: #fff;
    background-color: rgba(255,255,255,0.5);
}

Edited to add the default background-color (for browsers that don’t understand the rgba() notation). Albeit I was under the impression that all but IE do understand it (but I could be wrong, and haven’t tested to be sure…).

Edit with thanks to @akamike.

Edited to address question from OP (in comments):

which browsers don’t understand rgba? will they all in the future, is this part of css3?

The best information I could find is the CSS Tricks’ rgba() browser support table, with a link to a demo and ‘more complete’ compatibility table.