On the 1st of July, regions in Spain started issuing the so called "green certificates". These are your means to prove you have been vaccinated against Covid, have taken a test for Covid or have recovered from Covid. In other words your passport to travel within the EU and hopefully at some point to Britain.
To get one, you need to apply on this website. You will need to enter your SIP card details. Then you will be sent an SMS message to the mobile number they have on record with a code you need to validate your application. You can then download your certificate which has a QR code along with details of your vaccination status.