There are countless methods and approaches to calming the mind. Processes like anxious thinking repeat themselves over and over. So the question is how to stop that repetition.
One of the simplest, widespread approaches is mindfulness of breathing. When we are overwhelmed by emotions, our breathing becomes fast and coarse.
If we watch that, this awareness helps to calm down. First of all, we become aware of the tension in our breathing. If we have even minimal skills in relaxation (everybody has!), then we can calm down the tensions in our body.
(Often it's contracted diaphragm and the like).
So with love and attention we "send love" to the tense parts of our body. Wishing them to relax and to enjoy relaxation and calmness.
As a result, excessive tensions of body relax, and emotional tensions calm down too - at least to a degree.
Secondly, placing attention on breathing, we divert it from painful thoughts. It helps to let those thoughts extinguish.
That principle of withdrawing our attention from vexations is common for very many methods of calming.
My favorite is what I call Turtle Meditation. Did you see how turtles draw their paws and head under the shell?
Likewise, to develop tranquility, we withdraw from the object our emotions, our thoughts and our wishes.
It can be summarized in a brief phrase: "Don't feel, don't think, don't wish". Apply these three principles to the object that bothers you. Don't try to feel it, don't try to think about it, don't try to wish anything about it.
Note that it doesn't mean we should escape the real world and build ourselves a cocoon. The method is just to cut off the process of re-generation of vexations. When a problem needs to be solved, do it, don't escape; but when unnecessary vexation repeats over and over, then you will know how to stop it.
Maybe the only problem is that this method might seem counter-intuitive. We are used to think that concentration on our wish helps to fulfill it. Do you think so, right?
Indeed, often concentration is exactly what we need to achieve our goals. But when all the necessary actions are performed, what next?
Too often we remain concentrated on a problem - losing our time inefficiently, remaining tense, exhausting our body and especially our poor, self-torturing brain.
Did you notice that sometimes our strong wishing actually blocks us from receiving what we want?
Often it happens that we need to let the situation go - and then miraculously the fruit falls in our hands.
As Master Sheng Yen said, memorize the Four Steps of solving problems:
- Face it
- Accept it
- Deal with it
- Let it go
We need to apply strength of our muscles if we want to throw a ball, but in order to actually throw it we also need to release our grip, and it's better to do that just in time.
Memorize another advice from Master, which he admonished to apply both on retreats and in daily life:
- Abiding nowhere, give rise to the mind.
- Let all affairs come to rest.
I love to observe the world, to investigate what happens in the mind. Do you love that too?
Every child loves to learn. Only with time we lose that love for learning - some people to greater degree, some to lesser.
So another method for calming the mind is to supplement that calming with investigation. For example, if you can't reliably "turn off" your anxiety, can't let it go, then you can watch:
"Is that mental whirlpool helpful?"
Or: "Does this anxious concentration on the object of passion help?"
Observe. Then one moment a realization might strike, like a lightning in the dark. You would realize that this process of repetitive anxious thinking doesn't help anything.
And that realization will make turning your attention away easy. Moreover, this realization will affect your motivation. You will understand your mental processes better, and you will be less prone to developing unhealthy processes.
More likely your thinking will be healthy, your personality will become more joyful and unconstrained, people will feel your kind, free attitude to life, and so you will help others even by your presence - with calm, relaxed, easy-going mind.
It is said that all Buddhist practice boils down to the Three Highest Trainings:
You can find these three trainings in all the methods I described above. For example,
- persistently watching your breathing when you feel vexation is discipline;
- then sending loving care to tense parts of your body is calmness;
- seeing that your worries don't help and should be let go is wisdom.
In Buddhist practice, you can find many more methods and approaches. For example, Pema Chodron wrote several books on fear and anxiety, and how we can apply Buddha Dharma.
Regarding mantras: yes, we can use any mantra we like. All Buddhas are of the same nature, so Tara the Swift Savior helps as well as Compassionate Avalokiteshvara, as well as Mirror of Wisdom Manjushri, and so on. Some details see in my answer about chanting Buddha's name ("nembutsu").
Especially I love to practise Mahayana, e.g. the method of the Six paramitas (Six perfections). It turns our attention away from our worries and concerns about self, directing our life to helping others. As a result, our worries diminish. We realize that the world is big, and our problems look like a grain of sand in comparison. Our dramas look like puppets in a sandbox.
A brief explanation why Six paramitas help see in my answer about Buddhist healing.
The practice of Six paramitas is explained in details here: TheSixParamitas.pdf
Good health to all beings!