Traditional Plain Hunt

Plain hunt is the first "method" that a ringer is taught and is the hardest thing that they have yet come across. It is the building block of everything else that they will learn.

Firstly, what skill set does the learner need?

Lead competently
Speed up
Slow down

All of these should have been developed while teaching rounds and call changes. The change of speed is identical to that which they need to do when holding up to go back a place or speed up to go down a place.
It is worth noting that for the first time they can be changing places at backstroke as well. Perhaps try doing changes where the change is made on backstroke so that this does not feel too strange.

Terminology

Across the ringing community, the same action is described in a number of different ways just because you know what the terms are don't assume your learner does and try to be consistent with how you use them.

Leading - two blows (one whole pull) in first place. I don't think that there are too many variations on this
Hunting Out - each stroke (hand and back) move one place higher 1,2,3,4,5. Sometimes "Go out", "Out to the back", "Up to the back"
Hunting In - each stroke (hand and back) move one place lower, 5,4,3,2,1. Sometimes "Go in", "In to the front", "Down to the front"
Lie Behind - two blows in the highest place the last out stroke and first in stroke.

How to do it

Depending on the confidence of your learner there are a number of ways to teach this, explain what it is that they are going to be doing, from the lead change place each pull until they are in 5ths place and then ringing quicker each blow down until you are leading again.
Many people will argue against telling the learner the order of bells that they are following, I would not do this. The learner will be struggling trying to change pace of their bell, try and see who they are following, instead give them both pieces "2nds place over the two, thirds place over the four etc.".
I have tried teaching people as an intermediary stage to only change at handstroke, this then instills the order of the bells that they are following but the pace is "unnatural", my personal experience does not show this to be of any benefit, though that could just be my learners.
What will tend to happen is that the learner doesn't get high enough or doesn't come back down. Let the rounds settle down each time before trying again, and don't try a continue until the learner is getting back to the lead reasonably well.
Other than that it is just hard work and lots of practise.