I generally start by adjusting the Brightness/Contrast/Gamma/Color balance. It’s all one dialog box with a few sliders that you can access either from the menu (under Image—> Adjust…) or from a button that looks like some test bars above a slider.
Old photos tend to turn yellow. I initially attempted to just “cheat” and convert it to greyscale to counter this, but that wound up putting holes in the image as the computer couldn’t figure out the best shade of grey to use. Cranking up the slider on Blue tends to counter yellowing quite well.
Age also reduces contrast as the blacks lighten and the whites darken. A little tweaking of the Gamma and Contrast got me a picture with more definition that is generally greyscale, as a black-and-white photo should be. Gamma basically changes the darkness of medium shades without making whites whiter or blacks darker.
For certain sliders, it only takes a minor tweak to have a huge effect on the picture. On the sliders that go -100 to +100, I rarely go past about 30 points from center. Also, when I use those, I generally make sure the “Apply to image” box is checked so I can see the results in real-time as opposed to changing it, closing the box, finding out it’s wrong, and repeating that process about 27 times.
I wound up using Contrast 30, Gamma 0.80, and Blue 20 and got this. The brown stains are more prominent though, but that sort of thing is better handled with GIMP and takes long enough that you’ll quickly find out why those who retouch images for a living charge so much for their services. A filter is quick and easy, but manual touch-ups like those required to handle those cracks where the photo was folded take considerable time and effort.