I can't speak for everyone, but when I say 'prayer to the saints,' this includes 'asking the saints to pray for you.' The word 'pray' just means 'entreat', so when you see 'prayer to the saints,' read, 'entreaty to the saints.'
Are the prayers are answered? Yes. In order for a saint to be canonized in the Catholic Church, God must clearly have wrought a miracle through the saint who is being considered. The process whereby it is determine whether the miracle is genuine and whether it was the result of the intercession of a particular saint is a very rigorous one.
