How to allow registered users to change their user role through frontend?

I’ve edited the code a bit and this works on my localhost. Try it and let me know if it does the job.

Be careful to edit your own admin role though. Or put in another condition to prevent updating your admin role in case of a use error.

Edit: added ob_start() thanks to Mark Kaplun. Shortcodes need to be returned not echoed.

add_shortcode( 'upgrade_to_premium', 'upgrade_to_premium' );
function upgrade_to_premium() {

    // Stop if user is not logged in.
    if ( ! is_user_logged_in() )
        return;

    ob_start();

    ?>

    <form method="post" action="">
        Please select a role:<br/>
        <select name="role">
            <option value="subscriber" selected="selected">Subscriber</option>
            <option value="premium">Premium</option>
        </select>
        <input type="submit" name="submit" />
    </form>

    <?php

    // Do not process anything if it's not $_POST
    if ( ! isset( $_POST['role'] ) )
        return;

    // Never trust user input.
    $role = sanitize_key( $_POST['role'] );
    if ( ! in_array( $role, array( 'subscriber', 'premium' ) ) )
        return;

    // Get the user object
    $user = new WP_User( get_current_user_id() );
    $index = key( $user->roles );
    $user_role = $user->roles[ $index ];

    // User already got that user
    if ( $user_role == $role ) {

        echo sprintf( __( 'You already have %s role.' ), $role );

    } else {

        // update user role
        $user->set_role( $role );
        echo sprintf( __( 'Your role was changed to %s.' ), $role );

    }

    $output = ob_get_contents();
    ob_end_clean();
    return $output;
}