How much is the cheapest safety-deposit box?

I have no idea how they work, etc. Bear with me.

Depends on which bank, what size, etc.

I have one that is roughly 18"x 6"x 3" that is about $35 per year, but since I keep a certain minimum in that bank, the fee is waived.

Depends on your location and size required. Size really does matter.

When I lived in St. Louis County, MO, a small box approx 2x5x22 was about $40 at Bank of America.

In Warren County, 40 miles West, at a local bank, the same sized box is $22.

Guess it’s a matter of supply and demand.

Some banks will give you one for free, if you have a premium checking account.

Basically how they work (Actually, how mine works)

You apply for a box (yearly fees vary according to size) just like a bank account. You set it up with signatures and permissions for all who have joint priveleges.

They give you a key.

When you need to use the box you bring your key to the bank.
Present identification and sign a signature log.
You give a bank officer your key
You accompany the officer into the safe deposit vault
They insert your key and a bank key into the box release
They hand you the box
The officer takes you to a small privacy room that is in or near the vault. the officer leaves. In the room you can open the box and insert/view/retrieve your items.
When you finish you either place the box back into the vault or signal an officer to assist you.

The officer assists with handling the box but never sees the contents of the bax.