How do we open a dual flush cistern when spindles are not connected to the buttons?

You have to unscrew the spindles individually with your fingers from the base and they will pull out from the bar. They are screwed in so you can adjust the heights to marry up the flush mechanism with the buttons. Once you have removed the spindles you can grip the housing at the top rim with water pliers and turn that to remove it and then lift off the lid of the cistern.

Pull one of the flush buttons out and there is a screw underneath the flushes

If you are unable to remove the cistern lid and can't find any access screws to remove the button. Sometimes the button screws off in an anti clockwise direction or you can remove the button cap and you may find a screw under the button( be careful doing the latter incase you break the button)