Leave the menu, then immediately activate the bookshelf again. Activate the bookshelf, then place the desired book to be duplicated on it. This trick requires that you own a house with an alchemy lab. Leave the location of the mannequin, and go to a different area (for example, exit a house), then return to the mannequin to find the item still on the mannequin, which you can then take. Then, put the item back into your inventory.
Place any apparel item (armor or jewelry for best results) on a mannequin. Repeat this as many times as desired to get as much skill level gain as desired. Store the book on the shelf, then take the book back off the shelf, and select it, but do not read it. Read the Oghma Infinium book, then select the skill set to assign the skill gain. Go to your house, and open the bookshelf. Obtain the Oghma Infinium book, but do not read it. Please let us know about any of the content that does not work below.
Most of the content below will still work on the PS4 version, but some of the exploits may have been fixed. Note: All of the content below worked on the PS3 version of the game.