There are two ways to get what you want.
Link Manager
Go to wp-admin/link-manager.php, add a new link and enable the Links widget inwp-admin/widgets.php in one of your sidebars.
However, the link manager will be removed in the next version (WP 3.5). It will be converted to a plugin. I would not rely on it.
Custom Menu
Create a new custom menu in wp-admin/nav-menus.php, name it … Links and add custom links to it. Don’t forget to press Save. 🙂
Now go to wp-admin/widgets.php, enable the widget Custom Menu and activate the Links menu.
This will not change any time soon. I asked for it and I was told there are no plans to touch the widgets for 3.5.