There are a number of ways to customise / style the WordPress Login, but I find that our approach is the best.
1. Open up your child theme's (you are using a WordPress child theme right) functions.php and add the 'PHP' to your functions.php.
2. Create the CSS Style Sheet ‘style-login.css’ in the directory ‘CSS’ of your Child theme (if you don’t want a directory, or prefer to use a different name then change the function above. Add the 'CSS' to the new .css file: -
If your theme does not add a logo to the login, then uncomment the background-image and add your own. You can then adjust the proportions of the login image / logo via the width and height. The CSS ' background-size: contain;' declaration will ensure your logo is always contained within the specified size proportions. The above is the key basic styling, but you can adjust to your own needs by inspecting the classes on the login page and adding your CSS as necessary.