Obviously, these kinds of piano lessons are going to be the type of lessons we all grew up with, but there are a few tricks I've learned and apps to use that are important to implement.
The importance of landmark notes and intervals
Did you know that the treble clef's other name is called the G clef? Also, the bass clef's alternate name is the F Clef. The G clef used to actually be a G. The F clef used to be an F. Thus, the whole purpose of the G and F clef is not just to look pretty, their function is to identify where G and F are respectively. This should be taught to everyone! Until the student memorizes all the notes on the staff, the idea is to have the student memorize the "landmark notes," being the treble G, bass F, and middle C for both the bass and treble staff. Landmark notes can be more of course. When they are advanced enough, I like to teach them to memorize the highest line in the treble staff as F, and the lowest line in the bass staff as G. I also like to get them to memorize that 2 ledger lines above the treble staff is a high C, and 2 ledger lines below the bass staff is a low C.
After learning landmark notes, it is important to consistently require them to figure out the interval from the nearest landmark note to the next note.
GETTING GOOD AT SIGHT READING IS ALL ABOUT PATTERN RECOGNITION. INTERVALS ARE THE FIRST PATTERN TO TEACH THEM.
From an early age, and as soon as they have notes written on a staff (not floating in the air), I have them actually say as they play: "C, up a 2nd, down a 2nd, up a 3rd, same, down a 3rd," etc. Have them practice hands separately doing this as they play the next note. I have them say the first note of each line, then they say the interval and direction. If hands change at all, they also say the note again (it's not too helpful to have them say interval when switching hands or lines, because the point is to see what a 2nd looks like visually, what a 3rd looks like visually, etc).
Once they get to a point where 2 notes are played at the same time, hopefully they will have mastered intervals. You could even have them say the harmonic interval once they're playing 2 notes at the same time. But eventually too many notes makes it impractical to say the interval out loud anymore. However, intervals should constantly and consistently be taught as a way to find a note. For instance, if they get a note wrong, or if they ask what a note is, I will always ask them: "what's the interval from the previous note?" Train their brain to see intervals, and they will sight read very quickly.
I do not recommend using "every good boy does fine" or any of the like in order to memorize the notes on the staff. It takes too long. Until they memorize each individual note on the staff through sheer experience, have them use intervals so that pattern recognition is trained early in their brain.
Some methods use the term "skip" or "step" to describe 2nds or 3rds. I would highly recommend skipping this step all together (pun intended). The longer you wait to teach the intervals as numbers, the longer it will take for them to master them.
Note Rush app
Note rush is an app available for android or iphone. It is amazing as soon as they learn the staff notes. The app displays a note on screen, the student plays it on their piano, and the app uses the devices microphone to check to see if the note is correct.
There are 5 different levels, increasing in difficulty. You don't even have to use the levels if you don't want. If you're getting the student to learn very specific notes, then make a custom level for them. An example of a scenario would be if they are learning the C Major position (LH CDEFG RH CDEFG), but don't know the notes in between (the A and B below middle C). Level 1 quizzes them on more than just the C Major position notes. So you could create a custom level with only those notes.
Or you could make a level with just landmark notes. My favorite are below:
This guy is kinda creepy sounding but he gives you a good introduction to the app and custom level: https://www.youtube.com/watch?v=H0gQlaMZs8Y
This lady goes through the regular levels:
Using the custom level is VERY helpful because sometimes level 1 is even too hard, and sometimes level 5 is too easy when they get to a certain point.
Important to note is that the custom level is the only time the app quizzes them on sharps or flats. Levels 1-5 do not. So if you are introducing sharps and flats for the first time, and want to throw in a couple to test them, you'll need to make a custom level for them.
When level 5 is too easy, select all the notes in the custom level, including sharps and flats and natural notes. Set repeat to only 1 time (otherwise the level takes WAY too long) and make sure they are ready for it, because it can take upwards of 10 mins to complete if they aren't ready for it.
If their piano is heavily out of tune, they may have problems with the app. Also, the background needs to be relatively quite for the app to work well.
The app sometimes makes mistakes, although somewhat rarely. Sometimes it will just say a note is wrong even though the student hasn't hit a note yet, or sometimes say it's right without any input. So it seems to balance out :)
It is good to have the setting on that allows for mistakes to add 5 seconds to the student's score, it helps better gauge where the student is at.
If you have the student write down their progress throughout the week in their notebook, then you can know if they are ready for the next level or not. (I have them write down the stars they got and the time it took to complete the level. If I see almost all 3 stars, then they can advance.
Musictheory.net is a great resource for learning theory, but I use it for the interval exercise
Click on "exercises" at the top and click on "interval identification."