How to hide/show ‘out of stock’ products

1. In order to show out of stock products in Magento, perform the following steps:
   1. Open Admin panel of Magento store and navigate to System – > Configuration Section:
      
   2. Take Inventory tab from the left panel:
      
   3. Set Display out of stock products to Yes in Stock options tab in the right panel:
      
   4. Click Save Config button to apply the changes.
   5. Now you can see your products at the front end, even if the items are ‘Out of stock’.
2. In order to hide products on Magento store that are “Out of stock” or have QTY of 0, follow these steps:
   1. Open Admin panel of Magento store and navigate to System – > Configuration – > Catalog– > Inventory – > Stock Options Section.
   2. Set Display Out of Stock product to No:
      
   3. Click Save Config button to apply changes.
3. Clear Magento cache to check the changes applied.

Feel free to check the detailed video tutorial below: