First, you'll want to remove the default HubSpot styling from your form. To do this navigate to Contacts > Forms and click on the name of the form. Go to the Embed tab and check the box next to Remove HubSpot default styling. Then click Copy embed code and place on your external site.
Once you have the HubSpot form embedded on your external site, with the HubSpot default styling removed, you can style the form in your external site's CSS file. For a list of selectors used in HubSpot forms, check out this article.