How to cap a dead chimney?

Our chimney is no longer of use for us and we want to plug it up to prevent water and snow to get in and damage it such as it did last winter. No one around here seem to have any idea how to do it the right way. How do we go about pluging it up. It currently has a rain cap on but the snow and rain still get in. It needs to be done properly.

Thanks in advance.