The first is to recognize, more and more, that there are thoughts and feelings in my consciousness. This might seem obvious, but most of the time, we are just thinking and feeling without being aware of it. In other words, our consciousness contains thoughts and feelings, but not the awareness that we are experiencing thoughts and feelings.
By mindfully meditating on (i.e. observing) my thoughts and feelings, I can see that these thoughts and feelings just arise. They might simply come and go, or they might trigger a further series of thoughts, memories, or other associations. With practice, I have discovered that I can just release thoughts (and some feelings). Just let them go.
The more I meditate, the more I'm able to have this mindful awareness throughout the day, to recognize that I am experiencing thoughts and feelings. And when I notice negative thoughts, I can let them go.
There is a lot more to say, which is why mindfulness, meditation, and mental health are key themes of Losing My Religions. But as always, Bob Wright said it better in Why Buddhism Is True:
One virtue of mindfulness meditation is that experiencing your feelings with care and clarity, rather than following them reflexively and uncritically, lets you choose which ones to follow -- like, say, joy, delight, and love.