How do I keep notes about my customers?

At the bottom of the screen, there is a folder tab called Notes. It is there that you can write a free text note regarding your customer. 

This note is searchable from the search bar at the top of the Customer List View screen. 

The only thing that cannot be stored in a note is the customer's credit card information. If a customer wants you to keep their credit card on file, you can do so by adding their card to the "card vault".