Add New Dashboard Widget

Add a new widget to the dashboard. Note, this will add the widget to the bottom of the page. If you want to try to move it to the top, check out the Codex page about dashboard widgets

add_action('wp_dashboard_setup', 'add_custom_dash_boxes');
function add_custom_dash_boxes() {
    wp_add_dashboard_widget( 
        'welcome_box',
        __( 'Welcome', 'myplugin_textdomain' ),
        'welcome_box_text'
    );
}
function welcome_box_text() {
    echo 'Custom welcome text here';
}

Remove Unwanted Dashboard Widgets

If you feel your dashboard is too cluttered, you can use this to remove any or all of the widgets

add_action( 'wp_dashboard_setup', 'remove_wp_dashboard_widgets' );
function remove_wp_dashboard_widgets() {
	//Plugins
	wp_unregister_sidebar_widget( 'dashboard_plugins' );
	remove_meta_box('dashboard_plugins', 'dashboard', 'normal');

	//Right Now
	//wp_unregister_sidebar_widget( 'dashboard_right_now' );
	//remove_meta_box('dashboard_right_now', 'dashboard', 'normal');

	//Recent Comments
	//wp_unregister_sidebar_widget( 'dashboard_recent_comments' );
	//remove_meta_box('dashboard_recent_comments', 'dashboard', 'normal');

	//Incoming Links
	//wp_unregister_sidebar_widget( 'dashboard_incoming_links' );
	//remove_meta_box('dashboard_incoming_links', 'dashboard', 'normal');

	//WordPress Blog
	wp_unregister_sidebar_widget( 'dashboard_primary' );
	remove_meta_box('dashboard_primary', 'dashboard', 'side');

	//Other WordPress News
	wp_unregister_sidebar_widget( 'dashboard_secondary' ); 
	remove_meta_box('dashboard_secondary', 'dashboard', 'side');

	//Quick Press
	//wp_unregister_sidebar_widget( 'dashboard_quick_press' ); 
	//remove_meta_box('dashboard_quick_press', 'dashboard', 'side');

	//Recent Drafts
	//wp_unregister_sidebar_widget( 'dashboard_recent_drafts' ); 
	//remove_meta_box('dashboard_recent_drafts', 'dashboard', 'side');
}