Then when you make a change to your stylesheet you just have to simply change the version of your stylesheet to 2.
This is fine as it forces the browser to get the latest version as they see this as a different URL. But the developer has to remember to update this value every time they make a change to the stylesheet, which you can easily be forgotten. Another technique I've seen is to use time() to add the current timestamp to the end of the stylesheet URL.
http://example.com/stylesheet.css?v=<?php echo time(); ?>
The problem with this is that the URL will be completely different on each page load even is the stylesheet hasn't changed, therefore the browser will download a new version even if it hasn't got to. What you should be doing is getting the last modified time of the stylesheet file and add this to the end of stylesheet URL by using the filemtime() function.
<link rel="stylesheet" type="text/css" href="http://example.com/stylesheet.css?v=<?php echo filemtime($pathToCSS); ?>" />
Using With WordPress
To include a stylesheet in WordPress you should be using the function wp_enqueue_style() function (unless it's the main style.css file). This function takes a number of different parameters the 4th parameter allows you to pass in a version number that will be added to the end of the stylesheet URL.
add_action( 'wp_enqueue_scripts', 'add_styles' );
$css_file = get_stylesheet_directory() . '/css/style.css';
wp_enqueue_style( 'css-file', $css_file, NULL, filemtime($css_file) );