Look at this folder structure
https://drive.google.com/file/d/0B1_PFw--3o74WHNmMFlkRklKRTg/view?usp=sharing
Even on xamp or whatever install laravel using this guide:
http://novate.co.uk/deploy-laravel-5-on-shared-hosting-from-heart-internet/
Again in development and production use the guide, I recently used it for a shared host, the guide works 100% with zero problems.
Load your css using asset helper:
<link href="<?php echo asset('assets/css/dog/style.css'); ?>" rel="stylesheet">
Just correctly resolve your paths.
NOTE: My example laravel54up is "above" webroot, and laravel54 is under webroot (htdocs or www or public_html) depending on host.
Again develop this same way, with same folder structure.