Many used postage stamp needs to be removed from the envelope. A bowl of warm water and scissors are needed, and ordinary paper towels laid flat on a cookie sheet for the drying process. Press dry stamps between the pages of old phone books.

Steps

Decide to remove or keep the stamp on the paper. Some stamp supplies http://stampuoso.com/product-category/stamp-supplies are more valuable if they are kept on the envelope. An old stamp may be worth a few dollars by itself, but may be worth many times that in the historical context of the envelope that bears it.

Cut stamps off the corner of the envelope with some scissors

Place the cut corner in bowl of warm water and wait 10+ minutes. Apply cold water if you are worried the ink might run. In the past, some stamps were manufactured so soaking would ruin the stamp; this prevented people from illegally reusing them on new mail.

Most of the stamps will float off, so put them on the blotter of paper towels face down. Do this carefully so the stamps do not tear or crease. Some stamps require coaxing to come off the paper, especially the newer "peel and stick" versions.

Put the cookie sheet of stamps in a dry place (such as the unheated oven) overnight.

Place the now dry (and maybe a bit curled) stamps flat between the pages of a large book and weight them down if necessary.

Leave them for 3 weeks to be flat for handling and sorting into your collection, or for later use.

Some stamps, especially from the 19th and early 20th century, are preferable on the envelope, as it holds the value of the stamp
Plastic stamps take longer to soak off.
If you want to use washed stamps on an envelope, a glue stick will serve for putting them on. Use stamps that have not been processed through the mail. Using a stamp more than once for sending mail is illegal in most countries.
Use temperate water. Water with extreme temperatures might make the inks run on some stamps.