How can I purchase AppleCare for my iPhone?

Check out this page for info on AppleCare+. Make sure you choose your local region for the most applicable information on how to get AppleCare+ for Apple devices. https://www.apple.com/support/products/

If the notice appeared in the settings on your device, this would be how to set it up through settings: https://support.apple.com/en-ca/HT202702

In that case, you'll have to contact Apple support to discuss available options.