Warning: do not share your API key with anyone (including anyone at Airtable) since it's effectively a password that allows access to all your bases. If you accidentally reveal your API key, you should regenerate your API key as soon as possible at https://airtable.com/account.
To find your API key, navigate to your account page. At the bottom of the account page, there's an option to "Generate API key" next to a key icon.
Clicking this will generate an API key for you. Once you've generated a key, you have the option of regenerating a new key, or deleting your key.