Luton has only one terminal handling all airlines to all destinations.
Once you enter the concourse, you'll find check-in desks on the ground floor and security checkpoints next to them. There is no passport control on departure (at any UK airport).
A map of the terminal can be found on the airport's official website.
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Transfer between flights
As Luton Airport primarily serves low-cost airlines, it is not set up for direct transfers through the transit area.
So in most cases, you'll only be able to make a transfer here if you make it up yourself from two separate tickets. So you always have to go out, check in again and go through security back to the transit area.