My confirmation did not arrive

Three things to check before contacting the shop.

If your booking went through you saw an on-screen confirmation with a reference code. The email or SMS should arrive within a minute.

Check these first

Spam and Promotions. Confirmation emails come from noreply@mail.booked.co. Move it to Inbox once and future ones will land there.
The address you typed. A single typo in your email or phone number will silently misroute the message. The on-screen confirmation is the source of truth.
Carrier filtering (SMS). Some carriers hold the first automated SMS from a new sender for a few minutes. It will usually arrive.
Whether you gave an email or a phone number. Booked sends to the contact on the booking, and only that one. If you typed a phone number, nothing will arrive by email.
Whether you have replied STOP before. Texting STOP to a shop's messages stops all of them, confirmations included, until you reply START. See Stop receiving SMS from Booked.

Your booking is fine either way

A missing confirmation is a delivery problem, not a booking problem. If you saw a reference code on screen, the appointment exists in the shop's calendar. The message is a copy of something that has already happened.

If you wrote the code down, you can reach the booking at booked.co/b/ followed by the code.

If it still has not arrived

Contact the shop directly. They can see your booking in their calendar, correct a mistyped address, and resend the confirmation.

Reminders

Most shops send a reminder before the appointment as well. It goes to the same contact by the same route, so a confirmation that never arrived usually means the reminder will not either — worth fixing with the shop rather than relying on it.