It depends upon the brand of toilet. Some have the outer 'ring' unscrew, others have a hidden screw. If it's a dual flush button press one and keep it depressed. Then use a small flat headed screwdriver to 'pop' out the other button (carefully). You then take out the other button, and the screw will be visible underneath. If it is a single button, then usually you push the one button down, and keep it depressed, grab the outer 'ring' and unscrew (anti-clockwise), and yes it can be very stiff.
Fixit Fred..., January 2010