how do you get the top of the cistern?

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

I have two close coupled toilet cisterns and nieither are screwed on they just lift off. On one I lift it up around 2 inches and move it sideways to release the flush button arm from the flush plunger rod/square . When sorted guide it back in to the flush plunger rod the other one just lifts up clear as there are two rods the push the plunger down when flushing, one for full flush [larger of the two buttons] the smaller for half flush for urine dispersal.

BB
January 2010