The most important thing to remember during a mindfulness meditation is to not try to change your thoughts in anyway. The next important thing to remember is not to think that having thoughts is in any way a sign of failure.
There are four main things we can choose to be mindful of: thoughts, sounds, the breath and sensations in the body. The aim is to treat all these equally.
We should not be trying to change our breathing, nor our physical sensations and we should accept all the sounds we can hear in each moment. Similarly we should accept all our thoughts and not try to change them at all.
Thinking is just one of a number of experiences that happen in any moment and is simply one thing we can become more aware of in the present as we practise mindfulness.
Mindfulness may have an effect on our breathing, bodily sensations and our thoughts and we may feel a greater quietness despite the sounds we can hear but it is fundamental to the principle of mindfulness that we do not seek or expect any of these things to happen.
Mindfulness is about tricking the mind into a state of being and a state of being cannot be generated from a state of becoming, from an attitude of trying to change something.
This is why awareness, acceptance, allowing, letting go, relaxing, neutrality etc are key and often repeated phrases in a mindfulness commentary.
What we choose to focus on and the order we do it and what we become aware of, are all entirely irrelevant. The approach and attitude of simply being aware is the only aspect of any significance in a mindfulness meditation; all else is arbitrary and unimportant and simply a means to the end of gradually training the mind to feel comfortable and relaxed just being in the present moment.