In general, we want our photos to display a complete range of tones from black to white, but when it comes to retro effects, we can give the impression of a faded old photo by cutting out the two ends of the tonal range. This is easy to do with Curves (use either the Tone Curve in Camera Raw or Lightroom, or the Curves command in Photoshop).
Drag the bottom-left point of the diagonal curve line upwards slightly: this lifts our black point, so it effectively sets the darkest tone in our image. Similarly, drag the top-right point down slightly to fade out the white point.
To take it further, try similar edits on the red, green and blue curve lines. For example, drag the lower red point upwards to…