It is very important to develop a solid base when starting to learn piano without a teacher.
Bad habits, well practised, can stop your advancement early, ruin your motivation and will be very costly to re-learn later.
In the beginning it may seem that everything can be played by ear and reading music is not so important. But you can’t progress very far without understanding how the music is written down. Seeing the piece in writing helps to understand the general structure of the song as well.
Learning only one or a few pieces by ear would be more like a party trick, not really knowing how to play a piano. When you can read the music, you will be able to learn to play any songs.
For you, as a beginner, the first thing would be to memorize what notes in the score represent the keys on the keyboard. You don't have to play whole song by the heart, it is even considered a bad habit for a serious starting learner. You have to be able to find a piano key automatically when shown a note on the sheet.
For a practical approach, you should learn all the notes and corresponding keyboard keys, what appear in the songs you play. You have to be able to find keys on the keyboard without hesitation.
You have to be able to find a piano key without a hesitation by a note on the sheet.
The notes in the two octaves around the middle-C should come first. When all notes there are known by heart, then all the notes that are present on standard score lines (from F2 to G5).
The same is for other musical notations in sheet music, like tempo marks, sharps, flats, words in Italian etc. Learn them as they appear.
Good starting point would be to buy a music theory book and look up from there, when there is a new symbol or something is not so clear.
If the song seems overwhelming, then it is advisable to find some simpler songs and return later, when your skill has developed further.
Establishing good habits is one of the most important things for being able to progress and therefore keeping oneself interested. Correcting the bad habits is very painful later and needs a lot of motivation and time from both student and teacher.
Sheet music has finger numbers marked. If there are no finger numbers on some notes, the rule is to play the next key on the keyboard with your next finger. As a beginner, always follow these instructions.
Always follow finger numbers in the sheet music and play keys with the next logical finger.
Sometimes self-learners make extremely weird finger movements to reach the keys, for example bending and crossing the fingers under each other. This is not good. Only thumbs are allowed to go under other fingers.
Even if it may be possible to press the key this way, it wouldn’t be possible to get finger touch consistency and nuances needed for good and enjoyable piano playing.
Following the correct rhythm is the feature, what makes music melody to be recognizable for listeners. This is second only to playing the correct notes.
When student is concentrating on finding correct keys, quite often the rhythm gets lost. Therefore, it is very important to select playing tempo, where you are able to press keys at exact times and you can keep the correct rhythm.
Play slower than suggested tempo, if you can't find the keys and because of this can't keep up with the rhythm.
Play slower than suggested tempo, if you can't keep up with the rhythm.
When you are starting with a new piece, it is worth to look up a video in YouTube where someone plays this song on good level. In addition to just listening to the music, you should try to follow the piece in sheet music. For a beginner self-learner, it is important to notice what lengths the notes are played and how they are written.
When playing the same piece on piano, make sure, that you play notes with correct lengths and therefore whole song with correct rhythm. If you are not doing this, the song wouldn’t be the same.
You can record your playing and listen this yourself later. Then your feel of beat and rhythm wouldn’t be interfered with finding correct keys. You can hear, where improvement is needed and practise these bits separately.
Cultivating good habits is very important for progress, motivation and general enjoyment in piano playing.
I hope that these tips help you to enjoy playing your instrument for a long time.