I guess you mean people can put URL's on your site?
You'll have to check wether the URL does indeed contain an image-link, and not a piece of javascript that redirects your users to some kinky triple-X website.
You can use a few simple string-comparison functions, or a regexp, to make sure there's no javascript in it.
To find out wether it is a working URL you can do just one thing, and that is to fetch the url and see what you get.
You can use fsockopen to open a connectopn on port 80, then you can send a HEAD request and the remote server will give you a status code. 200 is ok, 404=not found, 500=no access etc etc.
If you also want to make sure it's an image, you'll have to download the entire file and see what you get.
a little more complex than you expected? :-)
A forum, a FAQ, email notification, what else do you need?