There are many ways to do this, but this is the way I've always done it. I have no idea about PS Elements since I've always used regular PS, but I imagine this process should be the same.
Make a copy of your image layer
Image > Canvas size (make sure to keep it anchored in the center)
Add the number of pixels you'd like the border to be
Fill the background layer with whatever color you'd like the border to be
Flatten image
That will give you a basic solid color border around your photo.
If you'd like an additional thin white border just around the image, before flattening simply select the image layer's transparency (ctrl-click on it in the layers palette) and Edit > Stroke
Choose your color/width
That would give you a thin border within the larger border.