There's an even simpler way, which works at least in current versions of Office (I'm not sure how far back in previous versions this is true).
Make sure the document and the photo file are saved in the same folder. In the document, press Ctrl+K (or click Insert > Link > Insert Link to open the same dialog).

The "Look in" box should already show the folder that contains both files, but if necessary you can navigate to the correct folder. Make sure the "Existing File or Web Page" box and the "Current Folder" box are selected. Click on the file name of the picture,
which will automatically be put into the Address box and the "Text to display" box. You can edit the text to display if you want the document to show something other than the file name. You can also click the ScreenTip button if you want to change the text
in the popup that appears when the mouse hovers over the hyperlink. Finally, click OK.
When the target file is in the same folder as the document, Word completely omits the folder path from the hyperlink. That means that when the hyperlink is clicked, Word will look only in the same folder where the document lives -- no matter whether it's
in the same location or on a different computer.