Alt tags are automatically added for you throughout the storefront on standard images.
If you want to add an alt tag to an image that you have added into a rich text editor (like in the product long description) then right click on the image in the editor, choose properties. You can then enter the alt text. Be sure to click save!
Beyond that, if you are using a custom skin, some edits to the skin itself may need to be made if you want to add alt tags to images directly included by the skin.