I usually don't answer when I have no idea, but I think here the correct answer is to have no idea. I have no idea what he means and a typical English speaker wouldn't either.

This is far from clear, but I guess he is saying "root him out like we would root out asparagus". The old-fashoined way implies by-hand, I guess. In this context, I guess that means follow him around as opposed to the modern way which might be searching computer files or something like that. Can I ask where you get these recordings? Is it part of a course?