<p>How can I check if a given string is a valid URL address?</p>

<p>My knowledge of regular expressions is basic and doesn't allow me to choose from the hundreds of regular expressions I've already seen on the web.</p>

The post
Getting parts of a URL (Regex)
discusses parsing a URL to identify its various components. If you want to check if a URL is well-formed, it should be sufficient for your needs.
If you need to check if it's actually valid, you'll eventually have to try to access whatever's on the other end.
In general, though, you'd probably be better off using a function that's supplied to you by your framework or another library. Many platforms include functions that parse URLs. For example, there's Python's
urlparse
module, and in .NET you could use the
System.Uri class's constructor
as a means of validating the URL.