Thomas Keating, the monk in the video is basically explaining meditation and much of Buddhism in Christian terms. The term he uses is contemplative or silent prayer. However, the monk glosses over a lot of important topics and practical techniques very quickly.
* He discusses the practical technique: 19:53–23:20 in the video. Notice how he says you go into the feeling of the body when negative emotions occur (this is key 21:12), and that you relax into the difficulties of life (again this is key). Also notice that you have to do this practice on a regular basis (ie: daily or weekly for a long time) and it slowly shapes you over time — especially when looking back at how you handled situations.
Also key is that when you are able to relax into some difficulty, life will throw something new at you — so your work of relaxing into these difficulties and doing silent prayer is ongoing (24:03–24:30).
* At 18:17–19:10 he talks about your attitude to difficulties. Notice that a beneficial attitude on difficulties of life is a result from the contemplative prayer practice — not the other way around. And that we are to welcome difficulties as learning opportunities.
* At 11:51–14:39 he explains why we have difficulties and negative emotions. It also explains a high level overview of the practice.
A great companion book to this topic might be Living Buddha, Living Christ by Thich Nhat Hanh. I have not read it, but know of the author.