I'm a bit confused about how, according to the Buddha, one is freed
Glad to hear you are interested in the end of suffering. Buddha laid out the Four Noble Truths as his very first sermon/teaching and they form the foundation of all Buddhist schools and thinking. Don't be fooled into thinking it is a pessimistic doctrine simply because it talks so much about suffering.
The basic idea is that everything in the world arises due to causes and supporting conditions. This is like saying that everything that you feel, see, taste, sense, smell, touch, and experience, arises due to causes coming together in the proper conditions. A cause is like a seed and the proper conditions are like fertile soil.. water.. sunshine. When all the conditions are there and the cause is present, there will be a result very naturally. This is the way things are.
Buddha taught, out of compassion for the plight of all sentient beings, that some actions (of body, speech, and mind) are wholesome and some are unwholesome. Those which are wholesome and virtuous are the causes of happiness, those which are unwholesome are the causes of suffering.
By abandoning that which creates the causes of suffering, and by acting in ways which create the causes of virtue, one is gradually eliminating the possibility of suffering to manifest in ones experience and increasing the growth and abundance of happiness, prosperity, joy, wealth, comfort, ease, and so forth.
Now, if you want to know more about what actions are harmful and which are helpful, you can read sutras and learn the teachings and thanks to our karma this life we have a good connection with the Buddhas and we can learn a great deal to eliminate what are known as the Obstacles and Obscurations from our mind streams.
Mindful awareness is indeed the greatest remedy of all. With consistent practice, virtuous actions naturally increase and defiled actions naturally decrease. One is no longer ruled or overcome by thoughts, and does not need to identify with emotions or thoughts, and one gains freedom from the extremes of "existence" and "nonexistence" as those are also just thoughts.
Historically, the Buddha laid out what is known as the Noble Eightfold Path. They are like 8 threads which weave together to form a complete solution to our how-does-one-live-a-good-life question. It is still very much about using our knowledge and understanding to make wise choices, but I think you would benefit from checking out this fundamental presentation of the way to the end of suffering.
Contemporary teachers and Buddhas of our day teach a variety of approaches, and so I would encourage you to develop strong aspirations to meet qualified teachers and sages in order to help you along the way. We are truly blessed to live in a world where the teachings are available and people are gaining interest in their value, and we are truly fortunate to have so many noble beings and enlightened masters living in our world today.
In short, practice being aware of your bodily sensations, your feelings, and the current instant of the world you are in where-ever you may be. Practice leaning into the awareness that recognizes and cognizes without identifying with what is recognized or cognized, and with consistent practice you will certainly see great benefits in your life.
Dharma is vast and there are many teachings one can read about but it is most important to put them into practice and really reap their value. To contemplate them and to put them into your daily life and actions.