Wordpress - How to create custom URL routes?

Add this to your theme's functions.php, or put it in a plugin.

add_action( 'init', 'wpse26388_rewrites_init' );
function wpse26388_rewrites_init(){
    add_rewrite_rule(
        'properties/([0-9]+)/?$',
        'index.php?pagename=properties&property_id=$matches[1]',
        'top' );
}

add_filter( 'query_vars', 'wpse26388_query_vars' );
function wpse26388_query_vars( $query_vars ){
    $query_vars[] = 'property_id';
    return $query_vars;
}

This adds a rewrite rule which directs requests to /properties/ with any combination of numbers following to pagename properties, with the query var property_id set. Just be sure to visit your permalinks settings page and save to flush rewrite rules, so this new rule will be included.

In your page-properties.php template, get_query_var('property_id') will return the property id if it was set, if it's not then show the default properties page.

Another way to do it:

add_action('init', function() {
    add_rewrite_rule( '^properties/([0-9]+)/?',
                      'index.php?pagename=properties&property_id=$matches[1]',
                      'top' );
}, 10, 0);

add_action('init', function() {
    add_rewrite_tag( '%property_id%', '([^&]+)' );
}, 10, 0);

Codex Rewrite API/add rewrite rule

Codex Rewrite API/add rewrite tag