You are correct, meatie.
The phrasal verbs are "walk|take {someone} through {something}" and "coach {someone} on {something}".
Allow me to me walk|take you through the stages of the process.
Allow me to coach you on the stages of the process.
The author has substituted "coached" for "walked|taken". This kind of substitution happens fairly frequently with phrasal verbs when the meaning doesn't become opaque because of the substitution.
P.S. The passage is not very well written. The clause beginning "making sure" is tacked onto the first clause. Passive voice strikes again. Someone who knows how to treat Ebola patients safely needs to coach staff on how to do it, and needs to make sure they have the proper equipment. Had the statement been phrased in that way, the reader might ask, "Who is that someone?"
P.P.S. Lest I be accused of being an active-voice bigot, let's look at an analogue of that poor sentence.
I need to teach him a lesson, making sure he remembers it.
He needs to be taught a lesson, making sure he remembers it. :-(
The clause in the original passage that begins "making sure" is written as if the preceding independent clause had been cast in the active voice. But it was not. The original sentence makes no better sense than the second sentence immediately above, about teaching him a lesson.