Normally, if you lift one of the two push-button sections up and then prize this out, you'll then be able to lift out the second part. After doing this, you'll then see a screw-driver slot in the circular push-button section. If you unscrew this, then the rest of the chrome-coloured push-button section will lift out and then the lid will be 'free' to remove and gain access to inside the cistern. HTH :o)
Nick from oddcolours.co.uk :o), April 2011