I've designed a site in PHP. I want to use CSS for handheld devices. How can I test it on my PC? And how a single CSS can suit most of the handheld devices. Do I need to compress the images used in background or do I need to create new images entirely for such devices? Very confused.

How can I test it on my PC?

The easiest way to do this is to install Safari and then you can set the user agent mode to mobile devices.

how a single CSS can suit most of the handheld devices.

It depends on your media queries and the meta tags, like this:

<meta name="viewport" content="width = 320" />
<meta name="viewport" content="initial-scale=1, user-scalable=no" />

Set that as needed for the devices you want to provide for.

Do I need to compress the images used in background or do I need to create new images entirely for such devices?

That depends, really, you could do either. Since mobile devices are often limited in bandwidth and people get charged for using that bandwidth, it's best to eliminate as many 'eye candy' images as possible. People visiting a website on a mobile device are looking for the content - not the decoration.