Note: This has been taken from the official installation instructions found here: https://wordpress.org/plugins/woocommerce/installation/
Automatic installation is the easiest option as WordPress handles the file transfers itself and you don’t need to leave your web browser. To do an automatic install of WooCommerce, log in to your WordPress dashboard, navigate to the Plugins menu and click Add New.
In the search field type “WooCommerce” and click Search Plugins. Once you’ve found our eCommerce plugin you can view details about it such as the the point release, rating and description. Most importantly of course, you can install it by simply clicking “Install Now”.
The manual installation method involves downloading our eCommerce plugin and uploading it to your webserver via your favourite FTP application. The WordPress codex contains instructions on how to do this here.
Automatic updates should work like a charm; as always though, ensure you backup your site just in case.
If on the off-chance you do encounter issues with the shop/category pages after an update you simply need to flush the permalinks by going to WordPress > Settings > Permalinks and hitting 'save'. That should return things to normal.
WooCommerce comes with some dummy data you can use to see how products look; either import dummy_data.xml via the WordPress importer or use our CSV Import Suite plugin to import dummy_data.csv and dummy_data_variations.csv.