According to your meaning, the melody should be played with the right hand and accompanied by the left hand. There is no right or wrong in art, only good and bad. Therefore, the accompaniment of the left hand is not unique and can be changed infinitely, but there are certain rules to be found. Generally speaking, the left hand is most commonly used in level 1, level 4 and level 5, which are all in major and minor tones, and are called orthochromatic level, which plays a leading role in arrangement. I suggest that we start with the monophonic accompaniment.

Take the melody in C major as an example, then the three notes of bass arranged by the left hand at different bars of the melody are 1, 4 and 5. You must start with monophonic arrangement. When playing, you should listen to the color change of music, and listening is the goal. Ear is the "best teacher" of arranger.

Music arrangement is a highly technical job, which requires more contact to get the gist. It is not an armchair strategist, but a theory and more practice. It is also suggested to look at relevant music theory books, such as basic music theory and simplicity and acoustics.