This is a Tibetan Buddhist mantra and visualization meditation. Tibetan Buddhist deities are depicted in very particular ways, with each nuance of their presentation symbolic of a way of being. The intended practice is not to pray to them like Gods, but rather to meditate on the way of being they personify, and through visualization and emulation, manifest this way of being.
Green Tara is always depicted with her left hand facing out in front of her heart, the thumb and ring finger touching in a mudra of love. Her right hand rests on her knee, thumb and first finger touching in a mudra of wisdom. Her left foot rests in half lotus on her thigh, symbolic of her transcendence over desire. Her right foot extended out slightly, symbolic of her readiness to help others. This speaks to the Mahayana Buddhist practice of awakening not just for your ourselves, but for the good of all beings.
A rough translation of the mantra is: OM: The sound of the infinite. TARE: liberation from all discontent. TUTTARE: liberation from fear and delusions. TURE: liberation from duality. SOHA: may the meaning of the mantra take root in my mind.
The practice is to visualize Tara above the crown of your head, being mindful of what she personifies as a being. While chanting her mantra, you visualize 3 lights coming from tara and coming from your won form as well. A white light at the brow point, a red light and the throat and a blue light at the heart. (Note that these colors do not correspond with the colors of the chakras.) The lights come in succession, eliminating negativity and obstacles in body, speech and mind. At the end of the meditation, you visualize Green Tara dissolving and merging through your crown and you take on her energy as your own.
It is good to dedicate your practice for the good of all beings when you finish.