I would suggest what xhtmlcoder said. Assuming you have a web page file (like index.html), a CSS file (like styles.css) and an image (like img.jpg), create a new folder on your desktop and copy them into that folder. Test that the files all still work by double clicking on the index.html file and opening it in your browser. If the styles and/or image don't appear, make sure that the links to the css file and the image are right (e.g. scr="img.jpg").
Then zip everything up and send it.
If, for some reason, there is still a problem with the image, you could upload the image to your own website (hidden somewhere), get its URL by viewing it in your browser, and link to the image there in your test page file. Then when your friend opens the page on his computer, he will see the image (as long as he is online).
You could even just stick all the CSS into <style> tags on the page itself, and link to the image online, so that all you'd have to send your friend is the index.html file as an attachment, not even zipped.