Custom search form to display users only

I am not going to write your form for you, but create a form and submit it to a page to do the processing, or use the AJAX API. Then use WP_User_Query to actually search for users. It is a very WP_Query-like class that should let you do everything you want including search for user metadata from the $wpdb->usermeta table by passing a meta_query parameter similar to the following from the Codex:

$args = array(
    'meta_query' => array(
        'relation' => 'AND',
        array(
            'key' => 'country',
            'value' => 'Israel',
            'compare' => '='
        ),
        array(
            'key' => 'age',
            'value' => array( 20, 30 ),
            'type' => 'numeric',
            'compare' => 'BETWEEN'
        )
    )
 );
$user_query = new WP_User_Query( $args );

If you have trouble, edit the question to include your (attempt at working) code and more detail, and I will edit the answer.