Do not pry the stamps from the paper - they will only be damaged. Then place the soaked stamps face down on the paper towels which will absorb lots of water and dry the stamps in about an hour. After they are all removed from the soaking tray, let them dry on the paper towel. 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. There are lots of empty spaces to put newer issue stamps and there is even some history about each stamp. Larger albums can contain up to 50,000 stamps and are massive multi-volume books. Now, how do you put stamps in an album.