$html = file_get_contents('path/to/file.html');
// Create a new DOM document
$dom = new DOMDocument;

// Parse the HTML. Use the @ to avoid any parsing errors if the $html string isn't valid XHTML
@$dom->loadHTML($html);

// Get all links 'a' we can use also 'img', 'li, 'table', etc to extract other tags.
$links = $dom->getElementsByTagName('a');

foreach ($links as $link){
    echo $link->nodeValue;
    // Full node
    echo $link->getAttribute('href'), '<br />';
    // the link itself
}