It's pretty easy to do, but not intuitive at all.
Select the media by clicking on it (anywhere - in the media tab at the bottom of the Person tab, or in the media box at the right side of the Family tab, or wherever. Just needs to be the most recently clicked on media image).
Then click the Media workspace at the top of FTM, and if it's not already selected, click the Detail tab in that workspace. You should see the image you clicked on earlier.
At the bottom of the page is the "Links" tab. Click New, then "Link to Person", and select the person you want to link it to. Now both people will show up as linked. Select the one you want to remove it from, and click the Unlink button (next to New).