Well, there is many way to change or edit or customize the WordPress admin page. Here, I will say about easiest way of the system. There is no need to gather technical knowledge to do the work. If you know how to click your mouse, you can do the work very fine. Yes, I am saying about a plugin name WP Login Welcome. This is a free plugin to do the changes. Just go here- http://wordpress.org/plugins/pit-login-welcome/ and install the plugin to your website. After activation the plugin you will see a settings page for the plugin. Click the plugin's settings menu than you will see the setting area. Plugin admin area is very easy. You can change WordPress Admin area's logo, background image, color easily just spend some clicks. Also there is a nice system available- Welcome Messages option. If you want to give some randomly messages to your users, you can do the work here. So enjoy the plugin. Thanks..
Nice plugin, but that's not the admin page: it's the login/registration screen. Just for clarity. The admin page is /wp-admin (the Dashboard).
Not the admin page, just Login as TIEro said.. Here is a plug that customizes the admin page.. http://wordpress.org/plugins/wp-admin-theme/
That doesn't modify the admin screen, either, apart from allowing you to mess with CSS. If you want to make actual changes to the dashboard without writing code, there's a variety of plugins, from messing with the widgets that show on the dashboard screen to closing/opening options for different user levels (Adminimize is one of the best options for that: http://wordpress.org/plugins/adminimize/).