Recognize your emotional reactions and the patterns of negative thoughts that trigger the depression or anxiety. You must learn to see them as soon as they arise throughout the day and during your session of mindfulness meditation. What you don't see is what controls you and creates suffering, therefore the first order of business is to become an expert in recognizing your patterns of habitual reactivity as they arise and not after the fact. In that moment of recognition there is a brief space, a seed of freedom and the possibility of change.
In Mindfulness Meditation Therapy (http://www.mindfulnessmeditationtherapy.com) you place the emotion at the heart of your attention and work on cultivating a non-reactive relationship with this object.
Reframe the reactions. You are not your thoughts or your beliefs or your emotions. All of these are simply objects that arise in your mind due to habitual conditioning. The trick is not to identify with any of them, and not to believe them to be inevitable, true, or who you are. Relate to each mental reaction as an object that you can observe and investigate, but without becoming ensnared in the contents. Simply stay mindful of the feeling tone of the thought or emotion, but do not indulge in thinking or emoting.
This allows a creative and therapeutic space to arise around the object, and it is in this space that transformation and healing takes place.
Stay with the emotion-thought-object. Sit with the object as you would with a friend in need. Mindfulness heals, and every time you embrace suffering with mindfulness it changes a little. This is the natural healing that comes from being fully present. Reactivity inhibits healing; mindfulness promotes healing. Its all about listening at the subtle intuitive level, without thinking or trying to figure things out. The engaged-presence of mindfulness is what does the healing.