Press either of the buttons on the toilet cistern all the way down. This will reveal an indentation on the face of the other button.
Use the edge of a flat-head screwdriver to carefully prise the "revealed" button straight off the toilet cistern. You should be able to lift the other button straight up with your fingers.
Use the screwdriver to carefully remove the holding screw located beneath the buttons. Twist the chrome ring that had been around the buttons up and off as well.
Lift the toilet cistern lid straight off, set it aside, conduct your repairs, then repeat the process in reverse to replace it. Make sure that the chrome button surround ring is correctly lined up, as it was, before replacing the buttons.