This is the most popular method for single-player worlds and is often used in glitch speedruns. It relies on a desync between the world save and the player's inventory.

Set up two hoppers pointing into each other so items cycle back and forth . Place the item to be duplicated into the hoppers.

The 1.7.10 dupe is a perfect lesson in —a classic computer science flaw. It wasn't magic or hacking; it was simply asking the server to do two things at once when it could only do one.