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.
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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.