Trying to turn off your brain is like standing on a board and trying to lift yourself off the ground - it doesn't work. Instead, become the observer of the thoughts you are having; allow them to be there, watching them come and go with acceptance and surrender, without trying to get rid of them. If you are very observant you can actually watch them as they form at a very subtle level of the mind before they are fully formed. When that happens they dissolve again right away. At some point an insight will come - "I am not my thoughts; I am 'here' (observing) and thoughts are 'there' (in the mind). What I am must be other than something thought based. What am I really?" This is called self-inquiry, and it is a powerful way of discovering your core essence. Knowing what you truly are frees you from remaining trapped in and identified with the mind, where "problems" originate.
Making this a daily exercise is best, even when things aren't troubling you. Take some time to sit down with eyes closed, relaxing into it with an attitude of exploration and curiosity, without expectation of attaining anything in particular, without any intention of ridding yourself of thoughts. Thought/mind is not to be demonized; thought is to be seen through as insubstantial and fleeting. What is it that sees this insubstantiality? That's what you truly are.
Another thing to explore is a more traditional "breath" approach, a type of mindfulness. Sit with eyes closed and put attention on the breath - feel it come in, being alert to its duration, then feel it go out; notice the pause between each breath - continue with this for 10 to 15 minutes. When you notice attention has been caught again in thinking put it back on the breath. Keep returning to breath awareness over and over, but never chastize yourself for any perceived failure - to "fail" at this is actually part of the process. Each failure is an opportunity to return to the breath, to return to awareness of what is happening. Over time you will find yourself becoming adept at keeping awareness there for longer and loner periods and you will discover as this happens that thought stream has diminished significantly. Rest in that thought free awareness and simply "be" - there is great peace and freedom there.