First you need to create that custom field and choose an apropriate name, then you can paste your link and save the post.
After that, you must open your single.php file (or the file where you want the link to exist) and insert the following inside the loop:
<?php
//first i select which custom field i want to get, i called it "my-custom-field-name" but you can change at your desire,
//it just needs to match the one you inserted in the post editor
$music_file = get_post_meta($post->ID, 'my-custom-field-name', true);
//here i define a title for the hyperlink, if you want to display a custom title, just define another custom field and adjust the name below
$music_name = get_post_meta($post->ID, 'my-custom-field-title', true);
//now i check if that field has something, that way if a particular post does not contain a link, no unnecessary html will be added
if ($music_file) {
echo '<a href="'. $music_file .'" title="'. $music_name .'">'. $music_name .'</a>';
}
?>
the code is pretty straightforward, but if you encounter any problems please let me know.
You can check more information about the get_post_meta function here.
EDIT:
To get the post thumbnail you must use the_post_thumbnail, read more about it here: the_post_thumbnail
First if your theme already uses the post thumbnails, you just include this <?php the_post_thumbnail( 'SIZE'); ?> in the size you can have: thumbnail, medium, large, full or a custom size defined in functions.php.
If your theme does not support the post thumbnails you must add this to functions.php
if ( function_exists( 'add_theme_support' ) ) {
add_theme_support( 'post-thumbnails' );
}