One of the first things you must do is to resolve not to throw it out. Then there is more...
I have often worked with age-fogged B&W paper with excellent results. The determinant here is just 'how' fogged it is. In the dark cut off a small (2" x 2") piece and place it on a table with a penny on it. Then expose to full room light for about 30 seconds. Then back to darkness and develop it for the normal time, stop, fix. Then look at it. How dark is the coin area? How black is the exposed area? The whiter the coin area the better off you are, obviously. This area is indicative of the extent of age fog.
Now, assume that the coin area is about midway between black and white. You are still safe here and can garner excellent prints. How? First, resolve not to develop for more than that required to bring the unexposed base density up to the midway level just stated. (If you go further you will not be able to properly 'bring back' that density to the original white without seriously destroying the image area.) If the unexposed area gets fogged beyond that point sooner than about one minute in the developer you must modify the developer to react slower which I do by adding baking soda. Try about 10 to 30 ml, measured (volumetric) in a cylinder (or 10 to 30g) as a starting point. That should slow things down. Then add the restrainer: about 15 to 45 ml of either a 10% potassium bromide solution or a 1% benzotriazole solution to the developer. Now you have a developer that will not allow the unexposed density to get too dark. This rather drastic 'solution', applies only to paper that is rather seriously fogged by age. Determine the time for development based upon not allowing the unexposed portion to get too dark.
Now that you have a proper development time you are in a position to determine the proper exposure by trial and error. The objective is to develop a print that is darker than normal because you will next reverse the excess density in Farmer's reducer after the normal stop and fix. It will take some getting used to but really excellent prints can be achieved with this method. The reason you allow development to progress long enough to get some density in the unexposed area is to allow proper contrast to build up in the print. The Farmer's reducer (used as a 'cutting' reducer by combining the sodium thiosulfate and potassium ferricyanide) enhances, or builds contrast. With age fogged papers achieving sufficient contrast is usually the most daunting task. - David Lyga.