Why and how would anyone store them for an indefinite period of time?
You wouldn't (well, there are some market conditions where you might, but it's not the norm). Commodities themselves are not traded on exchanges - what is traded are derivatives such as futures and options. And the physical delivery depends on the type of derivative that you trade.
There are two primary types of participants in the commodities market: hedgers and speculators
Speculators are easy - they are making a "bet" on the price of a commodity. They could bet that the price could go up or down, or that the price will be more or less volatile than the market currently thinks. In any case, they never hold the physical commodity. They either enter into cash-only contracts or they close their futures/options positions before maturity before they settle.
Hedgers are a bit more complicated. They are typically producers (e.g. corn farmers) or consumers (e.g. oil refineries) of a commodity. They may actually provide or take the physical commodity and transport it to or from the settlement location (e.g. the most common oil futures are contracts for delivery to a storage location in Cushing, Oklahoma).
Or, they may just use derivatives to hedge their exposure to the commodity price. For example, an oil refinery may use oil futures to "lock in" a price that they pay for the oil that they buy to refine (and may use gasoline futures to lock in the price of the gasoline that they sell). A corn farmer may use corn options to provide "insurance" against a drop in corn prices while still providing some upside if corn prices go higher.
I would also speculate (no pun intended) that the precious metal market is not significantly different than other commodities markets - most players are speculators or hedgers; very few participants (relative to the overall market) are actually buying and storing lots of gold.