If you want to change the way your Joomla site's password resetting or username reminding view looks, you have to edit Joomla's core files or create template overrides for those files.
The file for remind username view: \components\com_user\views\remind\tmpl\default.php
The file for reset password view: \components\com_user\views\reset\tmpl\default.php
Both files look almost the same. To alter the looks of the input forms, the simpliest way is to add a div around the form.
Add the CSS to your template's CSS file and youre done:
You can of course add your own CSS styles.
Hope this helps.