As with coin collecting, cleaning stamps, especially classic postage stamps, is not recommended, unless the cleaning is urgently required for the protection or restoration of the particular item. For example, the cleaning of buried ancient coins, to restore their original detail.
Recently I had a web inquiry asking if it was acceptable to remove toning from 1872 German definitive stamps with an eraser. Of course not, and it reminded me of the urgency of getting this important information about cleaning stamps up on my website as-soon-as-possible. I have personally committed such "sins" in the past, in trying to enhance the appearance of a newly acquired treasure, and in some cases, I wound up completely destroying the stamp.
Once I even tried cleaning some oily spots out of a nice used U.S. 1851 10c Issue by soaking it in a solution of soapy water, then repeatedly rinsing with clear water. It worked. But I later tried the same process with an Confederate States 1863 10c Issue. The blue ink dissolved and I wound up with a piece of very white blank stamp paper! The caveat? Artificially cleaning stamps, especially valuable classic postage stamps, can be very dangerous.
Up to 170 year old postage stamp paper is very fragile! Using an artificial cleaning device, such as an eraser, may damage the paper, the fine printed detail, or possibly tear the very fragile perforations on them. Cleaning stamps may result in the particular stamp having an "artificial" appearance, as well.
That's not to say you can’t "work" on your stamps ....
On a very large majority of my 19th Century used classical stamps, I have often used the method of soaking them in a dish of water, removing unsightly adhesions, and then drying and pressing them. Sometimes the stamps have lumps in them from old paper hinges or gum traces on the back, which can ultimately cause damage to them, if it is not removed. Even with some mint classical stamps, removing the gum is sometimes an option to preserve the stamp, as the gums of that era contained chemicals which could eventually discolor or crease the paper, destroying the paper the stamp is printed on. Mint 19th Century classic Austrian definitive stamps are very bad in this respect. This is even true of 20th Century stamps! Take a look at a Germany Hindenburg flight cover with the Hindenburg Zeppelin airmail stamp issue on it. Gruesome! The gum on these stamps contained "sulfuric acid"!
For simple soaking, just follow this process:
Many times this will result in a nice, fresh looking stamp, and it may even remove some paper toning. This method, is safe for most stamps, BUT, do some test soakings on cheap or damaged stamps first, to verify that the inks won’t run. For example, early British definitive stamps were printed with fugitive inks to prevent their reuse. Soaking or peroxiding these will cause the colors to run.
Paper naturally tones over many years .... as with currency notes, old newspapers, old paper documents, old books, etc. With my early US, years ago, I had a problem with toning and oxidation. Stamps printed in "red" shades are especially subject to oxidation. With my U.S. 3c 1851 issues, sometimes newly acquired stamps would appear almost brown, having originally been brilliant shades of Orange Brown and Brownish Carmine.
Another method for restoring the original colors from oxidation, or to possibly lighten age toning, is to soak them for a short while in Hydrogen Peroxide .... available at most grocery / drug stores. It works well with engraved postage stamps and with most lithographed or typographed stamps, but if the stamps are photogravure, you should be very careful. As aways, TEST THE PROCESS with CHEAP stamps first.
the stamp is an “expensive” one, I would suggest soaking it good, and
if that doesn’t work .... just leave it alone. I have destroyed very
valuable treasures in the past by unnecessary attempts at cleaning
stamps. If it is a stamp that you would have no issues about replacing
with another one, should something go wrong, then proceed as you wish.
If you don’t want to take that chance, then leaving it alone is probably
a good idea.