To allow your participants to pay by credit card, you'll first need to have Stripe linked and enabled as a payment method (under My Event -> Event Setup & Settings). PayPal is not currently supported for auction payments in particular.
Next, you'll also want to ensure you have enabled that payment method for your auction under Finances & Commerce -> Silent Auction within your Auction Settings:
So long as you have Stripe enabled and have accepted payments for auction items, winners will have the ability to pay by credit card once the auction ends. They will simply need to re-access the auction through the app (as a player) or through the link on your website (in the Menu at the top right).
When accessing the event, if they are not logged in, they can use the hamburger menu at the top right to do so:
Once they are logged in and are a confirmed winner, they will then see the option to 'Pay Now', which will ask them to enter their credit card information and submit payment.
Once paid, they will automatically be set to Paid under your Auction Reporting section and receive an updated Paid invoice to their email.