The cookie would basically just be a method of storing their username and password for future use. The login should just operate on sessions.

example:

<input username>
<input password>
<checkbox remember me>

Those would just be blank, unless they previously checked remember me. Then the cookie would auto-fill those forms.

The login wouldn't be changed though, if you have a session based login. A lot of people have cookie based logins, but I prefer session strict myself.

PHP: session_start - Manual