Do not pry the stamps from the paper - they will only be damaged. I place the soaked stamps face down on the paper towels which will absorb lots of water and dry the stamps in about an hour. Once dry, some of the stamps will tend to curl - this is not a problem. Get a few pieces of clean paper and place the stamps face down on once sheet and cover them with another. Some people place their stamps in a fancy albums.
Stamp albums come in a variety of shapes and sizes.
Beginners albums hold about 5000 stamps and most of the common stamps have pictures to help identify where the stamp is from and where to place it in the album. Larger albums can contain up to 50,000 stamps and are massive multi-volume books. Most stamp collectors enjoy their albums but I am going out on a limb and recommending to new collectors that they do not use a pre-printed stamp album. First off, they can be expensive and when you fill one you have a tedious chore of moving the stamps to another. Some don't give you enough room for all the stamps you collect from a given country.