Admittedly both here reproduce so small that it is difficult to tell that it's a photo of the Fairview Cemetery, but nevermind that. Here's how to work a similar job with Photoshop Elements (the cheaper version of Abobe Photoshop.)
1) Remove color from your picture by going to Enhance - Adjust Color - Remove Color.
2) Go to Filter - Blur - Surface Blur and blur as much as needed. The size of your picture will affect this, as will how sharp of a picture it was to begin with.
3) Go to Enhance - Adjust Lighting - Levels and tweek as needed to create a look like an old picture. If needed, proceed then to Enhance - Adjust Color - Adjust Color Curves and make further changes.
4) Use the Elliptical Marquee Tool and starting from the top left corner click and drag to the bottom right corner. Adjust the Feather option to a suitable number of pixels (this will depend on how large your photograph is.)
5) Go to Select - Inverse.
6) Use Filter - Blur - Smart Blur to blur the edges of the picture as much as you want for the effect.
7) Click off the Marquee, then go to Filter - Noise - Add Noise and as much as you need. Make sure it's set to Monochromatic.
8) Duplicate the layer (there should be only one layer at this point.)
9) Go to Filter - Texture - Grain to add grain to your new top layer. Set the layer then to Overlay Blending mode and Opacity 50%.
10) Now. Have ready a black and white picture of some scratches. Copy this and apply it as a new layer atop the others. Adjust the levels in Enhance - Adjust Lighting - Levels if needed, to create a crisp image.
11) Set the scratches layer to Soft Light mode at 80%. Don't fret if you don't see enough scratches yet, we're about to make magic happen...
12) Merge your scratches layer and your 50% layer. Now things should look like they came straight out of the video for NIN's Closer.
The following steps are optional (I did use them on the above example.)
13) Go to Layer - Layer Style - Inner Glow and adjust till you have the desired effect around the edges.
14) Flatten image.
15) Use Enhance - Adjust Color - Color Variations to achieve whatever tint you want over the photo.
And there you have it! Giving credit where it's due, this technique was adapted from the instructions at Alfoart's Photoshop Old Photo page.