Saving card data in Stripe with Cashier and charging later

I have been reading the Cashier docs, and I see how to implement Stripe using Cashier easily (and have already done so); however, I am confused about how I am suppose to be charging my customers.

My software's payment model is of a typical SaaS app in which a user sets their pricing tier (this will be the quantity of users they may add to their SaaS instance, so quantity is required for charging), and they are charged before use, and then on a monthly basis.

What I do not see anywhere in the Laravel Cashier docs is how I set the customer's card information, or how to hand them over to Stripe to do so.

Should I be handling user credit card information? I assumed the entire idea of Stripe was to separate the security and functionality of billing to a third party to make it safer for everyone.