If you are still interested after having read that huge title, sorry, I just couldn't put that in fewer words...
What I'm going to post here is a php function that will create a standard url from a user-inputted url so that any string will be converted to a functioning url.

First it will convert all characters to lowercase:

 
$url = strtolower($url);
 

Now add http:// if it is not at the beggining:

 
if(strncasecmp('http://',$url,7) !== 0){
	//There is no http:// at the beginning:
	$url = 'http://'.$url;
}
 

What strncasecmp does is it takes a string, and then a number. It then checks to see if that string is contained within the first (That second parameter) characters contain it. It returns 0 if it is found.
So in the example it checks to see if http:// is there, and if it is not, it adds it.

Now strip all folders (This is optional, but here I will show how to make sure only the main domain is left

 
$parts = explode('/',$url);
	if(sizeof($parts) !== 1){
		//no / in the string: (No http, no ending /)
		$url = $parts[2];
	}
 

So now we've got something like "http://{user_input}/".
Let's make sure it has (or not) www. And if not, let's add it (Just for consistency)

 
if(strncasecmp('www.',$url,4) !== 0){
	//There is no www.
	return 'http://www.'.$url.'/';
}else{
	return 'http://'.$url.'/';
}
 

Now we have "http://www.{user input}/" , we are basically done!
If you really want to this this correctly you could check if the URL exists, but this is just a waste of traffic from my point of view...
So if you want to do this, create the following function:

 
function url_exists($strURL) {
    $resURL = curl_init();
    curl_setopt($resURL, CURLOPT_URL, $strURL);
    curl_setopt($resURL, CURLOPT_BINARYTRANSFER, 1);
    curl_setopt($resURL, CURLOPT_HEADERFUNCTION, 'curlHeaderCallback');
    curl_setopt($resURL, CURLOPT_FAILONERROR, 1);
 
    curl_exec ($resURL);
 
    $intReturnCode = curl_getinfo($resURL, CURLINFO_HTTP_CODE);
    curl_close ($resURL);
 
    if ($intReturnCode != 200 && $intReturnCode != 302 && $intReturnCode != 304) {
       return false;
    }Else{
        return true ;
    }
}
 

And call it from our previous script:

 
If(url_exists($url)) {
     return true;
}else{
    return false;
}
 

Full code now:

So the whole thing would be something like this: 

 
//Function to make main domain from url:
function url_exists($strURL) {
    $resURL = curl_init();
    curl_setopt($resURL, CURLOPT_URL, $strURL);
    curl_setopt($resURL, CURLOPT_BINARYTRANSFER, 1);
    curl_setopt($resURL, CURLOPT_HEADERFUNCTION, 'curlHeaderCallback');
    curl_setopt($resURL, CURLOPT_FAILONERROR, 1);
 
    curl_exec ($resURL);
 
    $intReturnCode = curl_getinfo($resURL, CURLINFO_HTTP_CODE);
    curl_close ($resURL);
 
    if ($intReturnCode != 200 && $intReturnCode != 302 && $intReturnCode != 304) {
       return false;
    }Else{
        return true ;
    }
}
//And now the function
	function domain($url,$checkIfExists=0){
		//This function creates a url in the form http://www.domain.com/
		$url = strtolower($url);
		if(strncasecmp('http://',$url,7) !== 0){
			//There is no http:// at the beginning:
			$url = 'http://'.$url;
		}
		$parts = explode('/',$url);
		if(sizeof($parts) !== 1){
			//no / in the string: (No http, no ending /)
			$url = $parts[2];
		}
		//Now check if the url has or not www. in it:
		if(strncasecmp('www.',$url,4) !== 0){
			//There is no www.
			return 'http://www.'.$url.'/';
		}else{
			return 'http://'.$url.'/';
		}
		if($checkIfExists !== 0){
			//User wanted to check if exists:
			If(url_exists($url)) {
				return $url;
			}else{
				return false;
			}
		}
	}
 

So that is basically it!
(This function is used for example in my SEO analysis tool SE Crawler, to search for all documents in your site)