This is the same photo with the filter Aged Photo.
Photos can be aged in several ways in Adobe Photoshop. Some of the techniques hearken back to film photography, such as sepia toning. Others, such as Aged Photo, are new and specific to digital imaging software. Aged Photo, a preset in Photoshop, especially makes color photos look like they were taken in the 1950s or 1960s with color shift and softer focus. Since it's a preset, all you need to do is open the photo, go to Window > Actions and select Aged Photo.
This is a standard sepia-toned image.
The most common form of making a photo appear old is to sepia tone it. Originally, this was done with chemicals and had a practical application. When photos first were being printed in the middle 1800s, the silver that was used to produce the images was unstable and would fade relatively quickly. By sepia toning, which adds a reddish-brown tint to the image, the silver was replaced with a pigment derived from a cuttlefish. This makes the photos more stable, which is why most photos that survive from the era are sepia-toned.
This is a sepia-toned photo with Diffuse Glow added.
To sepia tone in Photoshop---if the image is color---go to Image > Adjustments > Desaturate. This will turn the image to grayscale, but keep the color information intact. Then go to Image > Adjustments > Variations. Using a combination of yellow and red, you can turn the grayscale image into a sepia-toned image. You also can take the original photo, go to Window > Actions and use Sepia Toning Grayscale or Sepia Toning Layer, but the former has a bit of a pink tinge while the latter has a bitter more orange. You can add a little more of the aging effect by going to Filter Gallery > Distort > Diffuse Glow.