How to display Woocommerce product price by ID number on a custom page?

If you have the product's ID you can use that to create a product object:

$_product = wc_get_product( $product_id );

Then from the object you can run any of WooCommerce's product methods.

$_product->get_regular_price();
$_product->get_sale_price();
$_product->get_price();

Update
Please review the Codex article on how to write your own shortcode.

Integrating the WooCommerce product data might look something like this:

function so_30165014_price_shortcode_callback( $atts ) {
    $atts = shortcode_atts( array(
        'id' => null,
    ), $atts, 'bartag' );

    $html = '';

    if( intval( $atts['id'] ) > 0 && function_exists( 'wc_get_product' ) ){
         $_product = wc_get_product( $atts['id'] );
         $html = "price = " . $_product->get_price();
    }
    return $html;
}
add_shortcode( 'woocommerce_price', 'so_30165014_price_shortcode_callback' );

Your shortcode would then look like [woocommerce_price id="99"]

Other answers work, but

To get the full/default price:

$product->get_price_html();

In woocommerce,

Get regular price :

$price = get_post_meta( get_the_ID(), '_regular_price', true);
// $price will return regular price

Get sale price:

$sale = get_post_meta( get_the_ID(), '_sale_price', true);
// $sale will return sale price