How to disable commenting from Twenty Ten theme?

WordPress admin screen -> Settings -> Discussion -> "Allow people to post comments on new articles". Uncheck it.

For existing posts, go to Posts -> All Posts. You can click "Quick Edit" on any post to find the "Allow Comments" checkbox and turn them off for that post.

To bulk-edit existing posts, you can select all the posts you want to edit at once using the checkboxes, then use the "Bulk" feature at the top of the page. Select "Edit" from the dropdown, click Apply. Then in the bulk editor, change the Comments dropdown to "Do not allow" to change that setting on all the selected posts.

This applies to any theme, it is not specific to Twenty Ten.

I believe this is fairly easy. You can disable comments in your WordPress settings.

Go to your WordPress dashboard -> Settings -> Discussion -> Allow people to post comments on new articles

You can also add the following to your themes functions.php to remove the 'Comments' page from the WordPress dashboard.

function remove_comments() {
    // Remove comments page
    remove_menu_page('edit-comments.php');
}
add_action('admin_menu', 'remove_comments');