The answer to this question depends of so many things but we have to begin somewhere don't we ?
First, a few answers
If one wishes to take private lessons or perhaps some other means of formally learning the piano, what are the topics that one must cover and in what order?
If we're talking piano lessons with any type of teacher, the teacher himself will have it's own technique or approach on how to play the piano. There are a lot of different things he can teach in a lot of different order.
Which topics are usually the hardest and thus need the greatest amount of concentration and practice and by one point along this line is a person at "intermediate" level?
Once again a question opened to a lot of interpretations. When do a piano player reach the "intermediate" level.. Who can really define what is an "intermediate" level ?
- Is it the middle point between a person who've never played and a person who made a career out of it ?
- Is it the middle point between what you know before you start and what you know when you reach the point your aiming for.
- Is it someone who can play a lot of easy pieces but not hard ones ?
Also, all of us piano players will struggle on different things when playing. I'll come back on it in a moment.
1 - The Pianist
- What is your goal as a piano player (playing for yourself or are you planning on making a career out of it )
- How much time are you willing to put in piano practice sessions ?
- What do you know about music in general ?
- What do you know about piano ?
- Have you ever played any other instruments ?
- How is your musical ear ?
- Do you understand that learning piano is a long journey and you probably won't play Chopin in a week ?
It might seem a little much to ask yourself all these questions but trust me, I decided to stop there because there are a hundred more that could define how long it would take you and where you would have to start.
Now that we've ruled out all the theory about how much your question is opened to interpretation, I guess you want some real explanations so let's start by implying you haven't touch a piano ever and you want to learn all by yourself.
2- Your piano
You haven't touched a piano yet. So what is the a piano. How does it work ? Why are there white and black keys ?
It might sound silly, but taking the time to sit in front of the piano and studying it for a few minutes without touching any notes is a good thing to do when you start. When you understand how the piano works (when you have a very general idea of how it works) you can start playing with it. How does it sound ? How does it react ? What is the distance between the keys. How long can I hold a note before I can't hear it anymore ?
Your going to spend a lot of time in front of it in the next months so the more you know about it the better. You can start playing with the pedals at your feet.
3- The techniques
At this point, and only now you should think about learning to play it.
- Scales (major, minor)
- Chords (major, minor)
- Exercises (I learned with a dozen a day which I highly recommand)
- Basic pieces
Now you should have a few weeks if not months of practice learning basic pieces and learning piano techniques that will always come in handy once you get better. Now you should be ready to enter the fabulous world of the piano. Don't forget, you can ALWAYS get better, and you can ALWAYS improve bits and parts there and there.
4- The beginner
Now let's try it my definition of beginner, intermediate, expert and professional (because everyone has there own definition of it) and how they should approach further learning.
I consider you are a beginner if you know all the things in point 3. If you've learned a few basic piece that don't require a lot of techniques like songs where both hands play the melody or songs with basic chords that goes along with the melody. If you feel a little adventurer, you can always pick up a piece like Solfeggietto and work on it for many days, you can have yourself a quite impressive piece to play with not a lot of difficulties in it. It is from the Baroc era so there is not any pedals (you can add some to help yourself or to make it sound cooler it's always up to you) so the song itself is not a big challenge. Also, it's very fun to play trust me it's one of the first piece I've ever played and I still love it today after 16 years.
5- The intermediate
Now you have a little experience in piano pieces. A few years or so. (This is still my own opinion on what is an intermediate player) You can play a lot of basic pieces and nothing you feel like your ready to move up in terms of difficulty. Basic chords, scales and stuff are no match for you you like to play them backwards to make it a little more challenging.
In my opinion, this is the fun part when you discover cool pieces you really want to play. You can handle a few more difficulties and you should head to a piece you like very much because chances are it's going to be hard to learn and master.
A piece I learned when I got to this part of my piano career is The Maple Leaf Rag. It's a very nice piece you're going to want to play faster and faster which is going to teach you to keep to what the score is telling you. You can either play it nice and slow with basically no expression or you can add every little details like on the original score and master it. You have a lot of time to spend on pieces in this category so once again I suggest you pick one you like.
6 - The expert
Usually the term expert would be on the top of the list but in this case, the expert is the one who played piano for a long long time. They know a lot and can play basically anything that comes in front of them. They've played countless pieces and are just below the professional career milestone. They can take challenges as hard as The Hungarian Rhapsody no.2 (I linked it because this version is worth taking a look at. From there all you can do is keep practicing and learning pieces you want. This is where I am in my opinion and I love it because I worked towards this point for a lot of years in my life and it finally pays off because I can play pretty much anything I want.
There is not a simple explanation that can be given on how or where to start learning piano and how to do it exactly because it depends of too many factors. Just never stop practicing it's the most important thing that will make you progress faster than any lessons or tutorials.
Good luck and I hope to hear one of you interpretations on the internet someday.