Passport control/customs Edinburgh to Madrid

The airline should be telling you how early you need to check in. It varies with airlines.
If you are flying with one of the economy airlines you need to print out your boarding "card" before you get to the airport. And you need to be at the gate at the specified time, or they will leave you behind.
Again, check and observe the airline rules.

You passport will be checked by the airline at check-in (unless you have a pre-printed boarding card), as you go through to security and finally at the gate by airline staff. The UK does not stamp passports on exit, but the airline has to report passport details and check your passport matches that on the ticket, so you will be asked to supply your passport details before you can get your boarding card, either online or at the check-in desk.

At Madrid you will go through immigration (passport control) for entering the Schengen Area. Depending on your nationality your passport may or may not be stamped.

There will be no customs as both the UK and Spain are in the EU. After picking up your bags go through the blue "EU" exit.

Thanks so much. Very helpful