Right click on the object and choose convert to editable poly. With the object selected go to the modify panel (little bent cylinder icon). At the top of the menu there are icons for vertices,edges,borders,faces,and elements. Choosing the last one will allow you to more easily select parts of the mesh that do not share vertices. Simply choose what you want to keep,invert selection (ctrl-i or edit/select invert from the menu) and delete, or choose what you don't want and delete. Hope that helps.