Lion’s Roar (a Buddhist magazine) has just published a good explanation of the Buddhist approach to mindfulness.
The article mentions the “four foundations of mindfulness.” These are instructions contained in a document first written about 2000 years ago. The foundations are:

– Mindfulness of your body. This could be of your posture, walking, breathing and so on.

– Mindfulness of feelings. This is about being able to observe your emotions and allow them to pass in their own time. it’s a really useful life skill which, I would say, we never really master but we can get better at it over time with practice.

– Mindfulness of the mind. You could think of this as being aware of your state of mind. So if your mind is angry you could realise this and also realise that this is going to heavily influence the kind of thoughts you have. Also, it can include being aware of your thoughts as they go through your mind. When you are aware of them, you can ask whether they are true or not, whether they really matter – and often they are not and they don’t.

– Mindfulness of the world around you. This is mindfulness of what you see, hear, smell, taste et cetera.
So as you can see the basic practices of mindfulness have not really changed in 2000 years. The article has much more than this and is well worth your time. Link.