First, make sure your Allmoxy instance is connected to Stripe (Settings -> Financial).
Then all you need to do is make sure your customer has a credit card saved as a payment method in the system. You can do this by going to their company page (either by finding them in your list of companies under the Contacts icon or by searching their name in the upper right hand corner of your screen). Once on their company page you'll click on info directly under the company name. Once you've clicked on that, there's a blue link in the Financial Management section that says "Manage Payment Methods." That's were you'll put in their credit card information. (Your customers can also do this themselves on their end).
You'll find invoices that need to be paid for by going to the customer's page and looking under the Outstanding Invoices section (example pictured above, has no outstanding invoices).