Sounds received through our right ear is mainly processed in the left brain half and sounds coming into our left ear are mainly processed in the right half.
You know if you are right or left handed, unless you belong to the very select group of naturally ambidextrous people who are equally at ease using their right hand or their left hand for all tasks. There is also mixed handedness, where some tasks are more easily performed with one hand and other tasks more easily with the other hand. But apart from these exceptions to the rule, most people are either right or left handed.
Reading and writing is so closely related to hearing and speech, that it is highly recommended to test for ear dominance when there are concerns in that area. Whilst it is quite easy to check for hand, foot and eye dominance, this is somewhat more complicated for ear dominance and in general specialist help will be required to test this.