How to list custom post types?

Here’s what I’d like to do:

a) Create a custom post type and write panel for a menu item called “My Stuff.”

b) “My Stuff” will behave like a category — but the content will not appear in the main blog. It will only appear under “My Stuff.”

So, what do I need to do? Create another loop? If so, where would I put the second loop, and how would I create a link to “My Stuff”?

Or should I add “My Stuff” to the loop in index.php, create a “My Stuff” category (or taxonomy) and filter “My Stuff” somehow so it only displays when certain fields are present?

Apologies for the complicated question, but I find this all very confusing. None of the scattered tutorials available on the topic clearly explain how to display custom post type content anywhere other than on a page or through the loop.

I’d appreciate any assistance.

Thanks.

a) Create a custom post type and write panel for a menu item called “My Stuff.”

Simple. The Codex should tell you everything you need to know.

But here is another example:

add_action( 'init', 'wpse_17863' );

/**
 * Creates a visible post type.
 *
 * Don’t forget to visit wp-admin/options-permalink.php once to refresh 
 * the rewrite rules!
 *
 * @return void
 */
function wpse_17863()
{
    $labels = array (
        // Usually plural.
        'name'               => 'Stuffies'
    ,   'singular_name'      => 'Stuffy'
    ,   'add_new'            => 'New Stuff'
    ,   'add_new_item'       => 'Add New Stuff'
    ,   'edit_item'          => 'Edit Stuffy'
    ,   'new_item'           => 'New Stuffy'
    ,   'view_item'          => 'View Stuffy'
    ,   'search_items'       => 'Search Stuffies'
    ,   'not_found'          => 'No Stuffies found'
    ,   'not_found_in_trash' => 'No Stuffies found in Trash'
    ,   'parent_item_colon'  => 'Parent Stuffy:'
    );

    register_post_type(
        'stuffy'
    ,   array (
            // visible
            'public'        => TRUE
            // Menu main name, usually plural
        ,   'label'         => 'Stuffies'
            // All labels
        ,   'labels'        => $labels
            // Menu position
            //   5 - below Posts
            //  10 - below Media
            //  15 - below Links
            //  20 - below Pages
            //  25 - below comments
            //  60 - below first separator
            //  65 - below Plugins
            //  70 - below Users
            //  75 - below Tools
            //  80 - below Settings
            // 100 - below second separator
        ,   'menu_position' => 5
            // permalinks
        ,   'rewrite' => array ( 'slug' => 'stuff' )
            // Create a default archive at /stuff/
        ,   'has_archive'   => TRUE
            // Allow child pages.
        ,   'hierarchical'  => TRUE
        // Add it to custom menus
        ,   'show_in_nav_menus'   => TRUE
        // Components of the editor.
        ,   'supports' => array (
                'editor'
            ,   'excerpt' 
            ,   'page-attributes'
            ,   'thumbnail'
            ,   'title'
             )
        // We use the built-in taxonomies too.
        ,   'taxonomies'          => array ( 'category', 'post_tag' )
        )
    );
}

b) “My Stuff” will behave like a category — but the content will not appear in the main blog. It will only appear under “My Stuff.”

I don’t understand this part. A custom post type may use a taxonomy – I added categories and tags in my example for a demonstration – but it isn’t one. You can use parent-child relationships tough like with pages.
I you clarify this point in your question I may be able to update my answer.

None of the scattered tutorials available on the topic clearly explain how to display custom post type content anywhere other than on a page or through the loop.

The parameter 'has_archive' is rather new. Older tutorials may not mention it.
To link to your new archives in themes or plugins use get_post_type_archive_link( 'stuffy' ).