What has to be done to be able to play the acoustic only on the neck with one hand without a pick or fingers in the other hand?
No amps included.
I think that's called finger tapping.
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If it's the fretting hand playing the notes, it's usually called 'hammer-on'. The usual strumming hand does it too, and that's often called 'tapping'.
With fretting hand, as the name suggests, fingers are hammered onto the frets quickly and firmly. Can be done with single fingers, or whole chords. Accuracy is the name of the game, 'cos once the finger hits the string, that's it. Much easier on electrics, but lots of players do it on acoustic.
Thinking about it, you may actually mean tapping with the picking hand. In which case, keep your sleeve out of the way, and use more of a whole hand movement, to get a bit more power into the hit.
A somewhat different approach, which makes sense to me, is to put the guitar onto your lap, while seated, and tap with both hands in a similar way to playing piano. Takes practice, but really works well.
What often accompanies hammer-ons are pull-offs, when the hammering on finger plucks the string after, in the same way that the picking finger would do.