You bought two keys. Only one of them is doing anything until you finish this.
An unregistered backup key is a piece of metal in a drawer. It becomes a backup at the moment it is registered to the same accounts as the first one, and not before.
Do it now, not later
The reason is circular and worth sitting with.
Registering the backup requires you to be signed in to each account. If you wait until you have lost the first key, you cannot sign in to register the second one, which is precisely the situation the second key was meant to solve.
Later is the one time this cannot be done.
The process
For each account you have already protected, go back to the same security settings where you registered the first key.
Add another security key. The flow is identical to the first time. Insert the backup key, touch the contact, enter the PIN if asked.
Give it a name that describes where it physically lives. "Desk drawer at home" or "Office safe" tells you something useful. "YubiKey 2" tells you nothing at the moment you need to know which one is missing.
Work through your accounts in order of importance. Email first, because everything else resets through it. Then password manager, finance, work accounts.
Set the same PIN, or do not
Two schools of thought, and both are defensible.
The same PIN on both keys is simpler and means you cannot fumble the emergency by misremembering which PIN belongs to which key.
Different PINs means a compromise of one does not hand over the other. This matters more if the keys are stored in different places with different levels of physical security.
For most people, the same PIN is the right call, because the failure mode you are likely to meet is forgetting, not theft.
Where the backup goes
Somewhere you can reach on a bad day, that does not share a fate with the first key.
Both keys in one bag is one bag away from having nothing. A backup at the office is not a backup on the day you cannot get into the office.
If you bought a Nano as the second key, its home is a desktop or a docked machine that stays put. If you bought a second NFC model, a drawer or a safe works, and it has the advantage of being handed to someone else easily.
Test it
Sign out of one account and sign back in using the backup key specifically.
This is thirty seconds and it confirms two things: that the key works, and that you registered it to the account you thought you did. Both are worth knowing before the day it matters.
Then check your coverage
Look at the list of registered keys on each important account. You should see two.
Any account showing one is an account where losing that key means account recovery, which is a worse afternoon than it sounds. Any account showing three is worth a look, in case one of them is a key you no longer have.
If you are still deciding which second key to buy, the two-key rule covers how to pick the pair.