Meditation is nothing but unbiased observation, that is: to see everything as it is. Mindfulness meditation is unbiased observation of the mind (thoughts, feelings, senses, etc).
The aim of this meditation is not to stop thinking or forcing the thinking to stop. First of all, accept that a lot of our thoughts arise without our intention. The aim is to allow such thoughts as they come on their own and to be aware of them and observe them without getting involved. Maintaining this distinction between you and your thoughts is paramount. Once a thought ends, stay in the silence until another thought arises, but make sure you do not initiate the next thought.
Observation of the mind is difficult. When you try to be aware of all your thoughts, you will find that a lot of times, you become aware of the thought after the it ends or in the middle of a stream of thoughts. For a moment, you were gone and only the thoughts were there. There was no distinct ‘you’ watching the thought. Try to realize this hypnotizing power of each thought- how it makes you become unaware and compels you to get lost in it. Sometimes you may become unaware for a few seconds, and sometimes, for minutes. But as soon as you realize you had become unaware, just keep on observing the thought without getting involved until it subsides.
There will be this cycle where you will go back and forth between being aware and not being aware of the thoughts. But with practice, you will get better at being aware of the thought as soon as it arrives in you. When you look at the thought in an unbiased way, you will discover that all your thoughts are completely separate from you. As this realization deepens, the hypnotizing power of the thoughts will start to decrease. I other words, identification with the mind will decrease.
But what will this achieve?
Freedom. From your own biases, fear, anger, etc. All the inner biases that blinded you will lose its power. For instance, when there is anger in you, instead of regretting your actions after you punch the other guy in the face, you will be able to recognize the anger and the compulsion of punching as soon as it arises. You would not get lost in those feelings and act out unconsciously and later realize what you had done. This was an extreme example, but life is very complex and offers many diverse challenges of this kind.
Time and place?
Any time and any place is apt for this meditation. You don’t have to do anything at all except being aware of what is happening in you.