Robert D Feinman

There are several software packages which help restore faded originals. Here is a way to do it with just the standard image editing tools.
This is the slide as scanned in without any adjustments. It was captured at 16 bits per color to permit editing without posterization.
It was taken by dad in 1947 probably on Anscochrome film at the Fulton Fish Market in New York City.
Notice the loss of density, especially in the cyan layer making the blacks turn orange.

The first step is to set the black and white points. I opened the curves tool and using the black eyedropper picked a spot in the wall at the lower left. Then using the white eyedropper I chose a spot in the top of the cloud at the upper right.
Finally using the grey eyedropper I picked a spot in the medium grey of the bridge roadway girders.

Here are the curves that this procedure generated. Notice how steep they are because of the loss of density in the original. Spreading the few remaining shades of color over a full gamut with only 8 bits would risk leaving gaps and thus produce a image with poor color gradation.
This shows the importance of using the largest number of bits per channel for the image when making such large tonal adjustments. Unfortunately Photoshop does not support adjustment layers on 16 bit images which means we must make all the changes on the image directly.
If we make a mistake we can always go back to a prior step or from a saved copy on disk.

Color Correction Curves

Because of the loss of density in the cyan layer the sky is still a weak blue.
We convert the image to 8 bits per channel.
Then using the color range tool we pick the sky color and make a new adjustment layer using saturation.
A small increase in saturation (about +10) and a slight shift towards the blue helps restore the sky to a more realistic color.

Unfortunately Photoshop does not permit using the selective color selection tool on 16 bit images, thus we had to convert to 8 bits first or use this technique on the 16 bit image.

Fix Sky

Just for comparison here is the original again. As a last step we did some dust removal and a small amount of cropping to get rid of the ragged edges.

Here is a full-size version in color.
Another interpretation in monochrome.

Maybe specialized software can make the task easier, but lots can be accomplished with the tools already at hand.

Original Again