If you have a website, you need a privacy policy and a cookie opt-in tool. If the website collects customer data i.e. has a contact form, it is more complicated.
If you don't have a website, then you don't need to ask customers to sign a privacy document, as you need their name and phone number, etc for "legitimate use". This means you has a business contract to supply a service or product. You need their private data for example, to book the appointment and call them to reschedule if you are ill.
This assumes you do not collect sensitive data like medical info - such as allergies. Otherwise you need to protect the data to a higher level.
You need to make a list of what customer data you have, how it is used, how it is stored, what you do if the phone or PC containing data is lost or stolen.
You need to have a privacy policy that explains the customers rights - for their data to be deleted, pause (not used, not deleted), modified or how they can get access to the data you have.
There is a lot more to GDPR, but I assume you are not sending email newsletters or have a webshop.