Upgrade to a premium account if you currently have a free account. You must have a premium account to be able to use stamps.
Find a picture of a Deviant Art stamp that you want to use. You can do this by doing a search for "stamp" or simply by glancing at the front page, where stamps are shown among the other art.
Click on the thumbnail of the stamp to arrive to it's gallery page. When there, go down to "share," right click on it and copy the "Thumb number." Thumb numbers are how Deviant Artists can share images.
Paste the thumb number wherever you want the stamp to appear. You can paste it in your Journal, your ID, in the forums and on your Deviation Page.