I try to cover several basic concepts during a first lesson. Posture/hand position, fingering, design of the instrument (patterns and pitch movement, and basic rhythm. (usually quarter and half notes is PLENTY, at first)
How much and how I present this information varies significantly. It often depends on the student's age, their focus and overall comprehension. It's KEY" to to make them feel that they CAN "WIN" and that they "CAN DO IT" from the start (with kids and adults alike).
The first thing is, posture and hand position. I differ with the notion that correct posture and hand position just "happens by itself", esp. with really young children, yet this is when it's most important. it's possible to be nice, and insistent at the same time! I positive reinforcement when there is a positive action. As teachers, it's important to be ever mindful of the following "It's not WHAT you say, it's HOW you say it".
Next, we discuss fingering, (R.H and L.H thumb is 1, middle fingers are marked as "3", an d so on) Usually, this takes no more than a couple minutes. With young children, this may take longer, but there are some fun, age-appropriate techniques to help them learn it quickly.
Basic design or "lay out" the groupings of the 2 and 3 black key sets. Starting at the low end of the piano with left hand fingers 2 and 3, they play all 2-black key sets. When they reach the middle of the piano, they continue up the keyboard with their right hand fingers 2 and 3.
They proceed to the 3 - black key sets in the same fashion using fingers 2-3-4. During this time, I ask what happens to the sound as they move up the keyboard. (Fortunately, in my 14 years of teaching privately, no one has given the answer, "it gets lower"!).
They're now ready to learn about quarter and half notes. I stress that they look different because they are different, and to please honor this accordingly.
In the first segment of the method I use, we look at short musical examples which use only quarter and half notes. Before they touch the piano, we tap (AND COUNT) the rhythm of each example. if the example is played with the right hand, I have them tap and count the rhythm with the Right Hand, and left hand accordingly.
once they seem comfortable, I introduce to them where middle C is located and to use it as a "guide" to help them find their position. The examples use the black keys only in the beginning segment of the method I use. There's a 'diagram" of the keys just above each example, of what finger goes on which key, with middle C being marked, which tells them where they need to place their fingers.
Once they locate the spot, they are ready to play. I stress keeping their eyes on the page, even if they miss something. (I guess it's a natural tendency for people to look at theur fingers whenever they miss something. To prevent this, I hold a notebook just over their hands.