Ultimately, your goal is to be able to listen to a piece of music and audiate it tonally. That is to say, when you listen to a piece of unfamiliar music, your ears should tell you:
The aforementioned skills are indeed the goal, but are decidedly inference skills that come with much practice. We are now going to practice distinguishing between major and minor tonalities using familiar patterns. This will give you the opportunity to learn how to distinguish between major and minor tonalities. This skill is called Partial Synthesis.
Since Partial Synthesis is an aural skill, it is difficult, nay impossible, to convey with only the written word. Watch the video Harmony Lesson 7: Comparing Major and Minor Tonalities.
The first step in distinguishing between major and minor tonalities is to listen for the quality of the tonic chord. This will give you your first clue to being able to identify the tonality. The very powerful process of hearing one tonality paired against the other will train your ears to hear the difference. Remember, we never learn what something is, we learn what it is not. In fact, that is part of the importance of discrimination learning: we learn major and minor and duple and triple concurrently so that we always have a means of comparison. We learn to discriminate between and among tonalities and meters.
After you have watched the lesson, try the Patterns-Only video below.
Finally, why not try a quiz? You should aim for at least 75% accuracy (15/20 correct). If you have achieved that benchmark, you can move on. If not, try going back and revisiting some of the earlier lessons.