Hey Brooks,
The shortcode should insert the form’s HTML code directly in place of whereever you’re putting the shortcode. This means that if you’re seeing any strangness, such as the form appearing in the background, it’s likely a conflict with the existing CSS in that region you’re looking to add it to.
One suggestion would be to use the ‘inspect element’ tool on a browser such as Chrome to identify the CSS styles that are in place on the plugin’s sign up form. In using that, you can identify which elements would need to be changed to adapt the form to your existing setup. For example, if it’s an issue with the width of the form, you may consider adding something to your stylesheet which sets the width of your plugin form to that hard-coded thinner width.
While implementing custom code and CSS is a bit outside our range of support here, if you have a link to a live version of your site which has the problematic form on there (being inserted by the shortcode), I’d be happy to take a look and provide some recommendations to get you started in the right direction.
-tk