Hello Jane and welcome to the Family!

As with any massive undertaking, you need to take it one step at a time. The first step is to learn how to handle stamps, then add and remove them from a page.
The point made by rod222 is absolutely essential, in that you need to learn to use a pair of stamp tongs (or tweezers, as the British call them). These are not the same tweezers you get at the drug store, but are a tool used by stamp collectors to keep from handling these wonderful pieces of paper with our fingers as much as possible.
The reason you don't want to handle the stamps is that our skin secretes oils which are transferred to the paper, and will, in the long run, damage the stamps. You also have less control with your fingers than you will with the tongs, as you become more adept at using them.
To start, if you have any U.S. used stamps from the 1940's and 1950's, this would be what I used to learn on. These stamps - with only one exception, the $5.00 black Hamilton from the Liberty Series, are all inexpensive and plentiful. Use these stamps to practice with the tongs. If something gets damaged, there is no loss. Also, use these to practice hinging them to pages and then a day or so later, removing them from the page. Knowing how to do both of these skills will allow you to begin mounting stamps in an album of your choosing and removing them safely from an older album/page.
My experience with removing stamps from a page shows the following to be the best procedure.
1. Lay the page flat. You don't want it curled when removing stamps.
2. Take the stamp tongs and slide one side under the stamp and try very, very gently to lift the stamp just a little. This tells you how the stamp is attached.
3. If the stamp will not lift or you cannot get the one side of the tong under the stamp - STOP. It is stuck to the page and will require more work to remove it.
4. If the stamp lifts easily from the point you have the stamp lifted, slowly slide the tongs up from the first edge you have lifted. If you run into any resistance, stop because something is hold the stamp in place. If when you look under the slightly raised edge, what has stopped your forward motion is a hinge, good - that's what you want. If it is the stamp itself stuck, STOP See note 3.
5. To remove the stamp, put pressure on the point where the hinge is folded, cutting it loose from the page. You will have a hinge remnant on the stamp. The stamp will now be free of the page.
There are many different types of hinges. Some were very user friendly in that they would easily come off a stamp while others would not. I never try to pull a hinge off a used stamp. Instead, unless it is a stamp with fugitive ink (There are not many of those), I give the stamp a soak in distilled water. This will dissolve the gum from the hinge, allowing it to fall off. This "bath" also will remove surface dirt and help tighten the paper when it dries.
To dry a stamp which has been soaked, place it carefully on a paper towel and place another paper towel on top. Place this under a book for 24 hours. When you remove the stamp from the paper towel the next day, it will be flat and clean, free of hinges and ready to be mounted.
It's best to work with a small quantity of stamps at a time, until you get used to working with them. Again, to start, use the U.S. commemoratives I mentioned earlier as they are plentiful.
Hope this helps!