Some stamps are better collected on the cover itself due to postal markings which to an amateur may not mean much. So check it out with a dealer or an advanced collector before soaking them.
Make a straight & neat cut around the stamp, leaving a small margin of paper on all sides. Soak the stamps face down in a plastic container (the breadbox transparent type) in warm water & after 30 to 45 minutes try loosening the paper from the stamp. You may find some the stamps still difficult to remove in which case leave them for some more time. Next put the stamps which are now free of the paper in another plastic container containing normal water for about 15 minutes. In this second stage of soaking the gum residue comes out leaving the stamp free of any stickiness. I generally take a third container filled with water & put the stamps in them for another 10 minutes before drying them on the back of a white blotter or a newspaper. Care should be taken in not being too hurried and rough with this delicate process. Stamps are weaker and much more fragile when wet.
You might find that your stamps will probably curl at the edges while drying out. This can be easily corrected by placing another piece of paper over the stamps once they are dry & placing a heavy object to weigh the down. Wait a few hours, or even a day, for the stamp to straighten out You will then have your desired stamp in great condition for keeps.
Note : Stamps on colored envelope paper such as greeting cards or bright colored ones should be soaked separately, as the paper often "bleeds" when it is wet & may cause irreparable damage to the rest of your stamps. Some stamps printed in fugitive colors (specially the earlier ones) are ruined by contact with water. The majority of stamps we see nowadays are printed using color fast inks that will not 'bleed' in water.
If you have mint stamps stuck together & you wish to retain the gum at the back then dont soak the stamps but use Lindner Stamp Lift which is available with me. It retains gum & leaves no traces & is safe, effortless & quick.