After flush water continues flowing into bowl?

Push button double flush. We are only getting the full flush, so how can we get the half flush working again and after flushing, water continues flowing into the bowl until we lift the cistern lid slightly, which appears to cause a wire to slightly move the flushing mechanism thus shutting off the water. Sorry to be so long winded - I'm used to a ball cock! Don't know make and model, but could find out. It would be really helpful if someone describes how these work in idiot language.