I have been a stamp collector for over 60 years. When I first started collecting I used stamp hinges to mount my stamps into my album. At that time, that was the only way to mount stamps. Years later, stamp mounts came out as a better way to mount stamps. Today, using stamp hinges will lower the value of your stamps. By using stamp mounts, you are not only protect your stamps but also keeping the value of yours stamps higher. Mounts come in both with a black backing or clear backing. Showgard, Kawid, Scott/Prinz, and Prinz are the major stamp mounts being sold. I personally use the Showgard mounts as I think they are the best quality mounts on the market.
I suggest that you put the stamp mount in the album first then put your stamp into the mount. You want to make sure their is no moisture inside the mount. Mounts come in two ways. Pre-cut and strips. To figure out what size mount you need first measure the horizontal length in mm then the vertical length in mm. Use a stamp gauge to measure the stamps which are available in this site. An example of one of the pre-cut mounts is the JV-25/40 which is the Showgard precut for vertical commemoratives. The 25/40 is width/height. Another way to order is to get the 40/264 strip and cut the strip to the proper width. Most collectors like to cut their own mounts. Their are also mounts available for full sheets and souvenir sheets