Alright you guys - trade secret time :
I (and many instructors that I know) let most of my first timers, and trial lessons that are actually interested, have a go at 'landing' the aircraft. Reason being that it's a talking point, makes them leave the aircraft feeling good and as such, more likely to come back for more. Truth is, the student is not actually doing jack sh!t in the landing phase but they don't know the difference.
Most instructors are able to fly the plane reasonably accurately using only little inputs on the foot pedals to control roll/yaw, and the trim and throttle for pitch. The unsuspecting punter is sitting there giving it the white knuckle death grip on the control yoke feeling like they're in charge, when in fact the instructor has it under total control the whole time. (Alright, it needs a very subtle nudge on the elevators at the flare phase, but it's barely noticeable and certainly not noticeable to the first time pilot, who doesn't know what a flare is supposed to look or feel like anyway).
I don't 'properly' teach landings until the circuit where it's supposed to be done, unless a student is particularly sharp and I think they can handle it ... but I get everyone following through my landings from about the climbing & descending lesson onwards (ie a couple of lessons away from the circuit), trying to show them the correct landing attitude and control position.
Hands off flying is a good skill for all pilots to have, it teaches you loads about the proper use of balance and trim, and not to lean on the controls for support while you're distracted inside the cockpit (i.e. not watching attitude). In the past I've made students who are up to the cross country nav phase and haven't learned how to trim the aircraft properly (i.e. most of them!!) fly an entire cross country flight without touching the controls, using nothing but trim and rudder, seeing how long you can keep it accurately on height and heading for - most of them find it's much more accurate than their normal rough, two handed flying.
RHA, you'll find that it all relaxes after a few trips. If you're like most people, you'll be tending to grip the controls two handed and pull back on them for support with every little unexpected movement of the aircraft at first, it's totally normal. Try not to stare at the instruments or out the sides too much because that is what makes it disorientating, just focus on really trying to relax, visualise and set the correct attitude your instructor is trying to show you out the front window.
Cheers
L.S.T.