For more information about hiding out of stock items from individual categories, please see this help article - http://help.crystalcommerce.com/en/articles/1389584-creating-categories
If you want your customer's search results on your webstore to not show any of your out of stock products:
Go to your Admin > Accounts
Click on the Frontend tab
Here, you will see a Hide out of stock products in search result? option.
Check it, and Save.
Once you do, products that are out of stock in your admin will not be part of the search result outcome.