need to stop out of stock from displaying

How do you stop out of stock products from showing up in your catalog?

Set them to;
Product is: In Stock Out of Stock

when editing them ...

Or, you can click on the Status icon ... Green is In Stock and Red is Out of Stock ...

You can configure your shop in the Stock settings so that when a products_quantity hits <= 0 it is set to products_status = 0 which is Out of Stock and it will not display in the Catalog ...

NOTE: this will take affect on NEW orders that set products_quantity <= 0 but not on past orders to affect Products that already have products_quantity <= 0 ... you will need to update those products either manually or with a global command for this that you can run in the Tools ... Install SQL Patches ... of your Admin