First of all create a custom Login Form, to make it little bit easy create a custom template
Then you have to make a login form into your template.
Now use wp_signon() to make the user login, take a look on this example:

$creds = array();
$creds['user_login'] = 'example';
$creds['user_password'] = 'plaintextpw';
$creds['remember'] = true;
$user = wp_signon( $creds, false );
if ( is_wp_error($user) )
    echo $user->get_error_message();

If you want to customize the current wordpress login page (usually wp-login.php) you should take a look at WordPress Codex for Customizing the Login Form.

Or if you want to create a separate login page for your theme, I suggest you to use Theme My Login to do this.

This plugin themes the WordPress login, registration and forgot password pages according to your current theme. It creates a page to use in place of wp-login.php, using a page template from your theme. Also includes a widget for sidebar login.

Plugin Features

• Your registration, log in, and password recovery pages will all match the rest of your website
• Includes a customizable widget to login anywhere from your blog
• Redirect users upon log in and log out based upon their role
• Show gravatar to users who are logged in
• Assign custom links to users who are logged in based on their role
• Customize user emails for registration and/or password recovery
• Send user emails in HTML format
• Allow users to set their own password upon registration
• Require users to be approved or confirm e-mail address upon registration
• Theme user profiles