Step One

Create an image with 2x the resolution of what the final image needs to be.  If you are creating for the web the final resolution will be 72 so create the image at 144.

Step Two

Open the image in PhotoShop.  Use the Rectangle Marquee tool to create a select  box around the area for the cut out.

 

Step Three

Save the selection using the Selection menu and the Save Selection option.  In the Save Selection dialogue box give the selection a name.

Step Four

Use the Edit menu and copy to copy the selection then use the Selection menu and deselect to clear the selection.

Step Five

Reduce the resolution by using the Image menu and Image Size selection.   The new resolution should be 1/2 of the original resolution.

Step Six

Use the Edit menu and paste option to paste in the cut out box.  The cut out box is still at the old resolution so it will be 2x its original size.  Use the move tool to position the cut out.

Step Seven

Next a border will be placed around the cut out.  In order to make the border the cut out needs to be  selected.  The cut out is on it's own layer, so take a look and make sure the cut out layer is active.  Next use the Magic Wand tool to select everything but the cut out.  Next use the Select Menu and Inverse option to select only the cut out.  To add a border use the Edit Menu and Stroke option to create a line around the selection.

Step Eight

Next create a border around the original area.  Use the Selection menu and the Load Selection option.   Choose the selection that was saved in step three.  Next use the Edit menu and Stroke option to create the border.