1) Saving a table with a bunch of true/false values on whether or not a player owns an item.
2) If it's possible (I'm 99% sure it is), save the items themselves.
Neither, if a player has an item, save the items name as a string in a table then run a loop and load all the items the player has by checking with the string.
@spinywind Thank you, I'll be sure to use this method. But how do games like Miners Haven and Sandbox save everything about where and what your placed stuff is?