Under Shop settings, Booking rules, Cancelling and payment, switch on Save their card when they book online and type your fees: a no-show fee, a late-cancel fee, or both. Late means later than your cancel window above it, so a late-cancel fee needs one. Each fee is at least 30p, the smallest card payment. It needs your own Stripe account connected and verified, as deposits do.
On your booking page the customer sees your terms before they book, in your own words for the trade. For example, "Your card is saved, not charged. If you miss your appointment, Hair by Jo may charge 20.00. If you cancel less than 24 hours before, Hair by Jo may charge 10.00." When nothing is due up front they press Continue to add your card and add it on Stripe's page, and nothing is charged. When the service takes a deposit or the full price, the same payment keeps the card. The booking keeps the terms exactly as they agreed to them, so changing your fees later never changes what an existing booking can be charged. Their confirmation email and their booking page show the card (for example Visa ending 4242) with the terms. The card is kept by Stripe on your account; FullDiary never sees the number.
If they do not turn up, mark the booking No show in the diary and press Charge the no-show fee. You see the booking, the card and the fee they agreed to. Charge all of it, or choose Some of it to charge less (never more). Customers cannot cancel online inside your window, so a late cancellation is you cancelling after they ring. When it is late, Cancel asks Who asked to cancel?, and They did charges the late-cancel fee as it cancels (untick it to let them off). If they paid a deposit, They did keeps the deposit instead and charges no fee on top. The fee comes back only if you choose to refund all of their money. Once cancelled, Charge fee is beside the booking in their history under Customers. The money goes to your Stripe account, and the customer is emailed a receipt quoting the terms. If their bank wants them to approve the payment, or turns the card down, they are emailed a link to pay it themselves with any card instead, and you are told so. If they cannot find that email, Email the link again on the booking sends it again. One fee per booking, and the same place offers Refund to send it back to their card.
This works for appointments booked on your booking page, not yet for classes or several bookings paid together, and it is on the website for now. In the FullDiary app, the settings and Charge fee are still to come. A fee shows on the booking, in your activity log and in your Stripe, not in your dashboard takings, which count finished work.