In piano, generally, the right hand has a more melodic role, while the left hand is rather attuned towards harmony. In other words, the right-hand plays the melody, the left hand the chords. It is obviously not as simple as that. In so-called contrapuntal music, for example, the sharing of functions is much less accentuated.
You will notice that it is much easier to play with the right hand than with the left hand. The left hand is clumsier, less strong too. At the start, you will tend to only play with the right hand (this especially concerns right-handers).
Starting with the right hand is not so serious since it plays the melody, that little tune that we remember when we hear music. However, to fill out the music, the left hand becomes essential.
If you begin to learn the piano on your own, you will find that it is easy to learn the melody first. Once you perfect the melody, you will have to focus on other aspects of the piano. It is a method like any other. Everyone must find the learning method he/she is comfortable with. However, you will not be able to avoid training with your left hand.
Succeeding in gaining independence with both hands will therefore mainly consist of you, at the start, in playing the left hand. How to play the piano with the left hand? Or rather: how to learn to play the piano with the left hand?
To solve this first obstacle, the solution consists of starting by playing with the left hand only (for example, play scales with just the left hand). Do this from the start of your piano training. Do not wait two months before working with your left hand. You have to deal with this from the start of your piano study.
Once you are more comfortable with your left hand, you can start playing with both hands together. Therefore, the trick is to not start playing with both hands before you have worked on your left hand alone.
To progress, start by playing the same notes, with the same times, with your right hand and with your left hand. You then play exactly the same thing with both hands. Then learn to play a very simple score, each hand having a different part. Above all, start by working with separate hands. It is indeed another rule to respect, do not play both hands straight away, but first work with separate hands.
Slowly take in the notes and take the time to remember the tones. Your brain will do it on its own over time. There is no point in hurrying to learn a song, as it will only discourage you.
You will see that with the independence of both hands, playing hands together will be less and less challenging. It takes time for your brain to form and your hands to memorize the movements.
You can take help of a professional piano teacher in Vancouver BC to help you use your both hands independently while playing the keyboard. It will take you at least a year of practice to become truly capable of gaining good independence with both hands. So don’t get discouraged too quickly. You don’t become Mozart overnight.