The individual graphics can then be displayed by appropriately positioning the graphic as a background image at the desired location.
That sounds complicated and requires a lot of fine-tuning. It would be without the following useful tools:
Optimize Website: If you want to equip an existing website with CSS sprites (which I recommend to everyone), the SpriteMe tool can help.
Simply go to spriteme.org and drag the link displayed there into the bookmark bar of your browser. You can now call up the tool by clicking on the link.
It then analyzes the currently open website and suggests a sprite combination which can be downloaded directly as a finished graphic.
SpriteMe also generates the appropriate CSS code, which you only have to include on your website together with the graphic.
Sprite graphics from individual graphics: In order to automatically generate a Sprite graphic + CSS code from individual graphics, you simply upload your graphics as ZIP packed to the CSS Sprite Generator. The tool does the rest.
Generate CSS from Sprite Graphics: If you have already made a Sprite graphic yourself and now want the appropriate CSS code to address the individual graphics, you can use Sprite Cow.
There you upload the graphic, select individual elements and the CSS code is displayed immediately.