No worries about being new, nobody actually answered your question so far.
When you buy a spell book, it shows up in your inventory. There's a control for reading books (and other written things like letters, recipes, notes etc.) from your inventory. I don't know your platform so I can't tell you, but look for the on-screen instructions.
When you read a spell book, the spell is added to your available list under the magic section of the main menu. A fireball is listed under Destruction spells etc. Open the main menu and navigate to the Magic section, navigate to the category you want (Destruction, Restoration, Conjuration, etc.), find the spell and select it for your left hand or right hand. Again, look for the on-screen instructions.
When you read the book, it is destroyed and disappears from your inventory. If you try to read it and nothing happens, that's because you already have the spell.
Ok? Good luck have fun!