This is actually a fairly simple task — although many of the Photoshop authors make it seem more difficult than it really is. Using logic, the portion of the image to be popped out of the frame must be separated from the original image and raised to a higher level, in front of the frame, while leaving the original photo in tact. This technique works in any image software which has layers.
1. Cut out the image: Using any of the software's selection tools you wish, make an accurate selection of the portion of the image you wish to pop.
In this example we used a combination of the Lasso and Magnetic Lasso to carve out the front of the car. Tip: to save time, cut only the part that will pop out.
Lift the image: Once your selection is accurate, and ready to go, duplicate it onto its own layer by using the "float" command (Cmd/J or Ctrl/J)
You can see the nose of the Jaguar is now on its own layer. (#1 in the layers palette) Note that it's just the nose — no use to select more than you have to. It will match perfectly with the original image on the background layer and provide a seamless pop-out.
2. Create the Frame: Now, in a new layer, you can create the frame for the photo. Here we simply used a white background with the frame cut out. Layer #2 in the diagram.
At this point you can decorate or modify the frame any way you wish — textures, borders, etc.
Key Concept: Layer Sequencing. Always remember that the stacking order of your layers affects the final product. As you look at the file, you'll understand that the layers were generated in that specific stack order to achieve the effect — even though they may not have been created in that order.
Also note that we did all the selection work on a COPY of the background, just in case we flubbed something up, or needed to go back and get more of the image. The "work" layer can be deleted, and the whole image flattened when complete.