Popular ways of invoking Avalokitesvara
念彼观音力
By reciting his sacred name:
南无观世音菩萨
(chinese)Namo Avalokitesvara Bodhisattvaya (sanskrit)
Homage to Bodhisattva Avalokitesvara (english)
Or by reciting his mantras:
Om mani padme hum
The Tibetans' favorite mantra, known as the mantra of 6 syllables 六字真言
Om aroliku svaha
This is known as the mantra of Aryavalokitesvara 圣观音 the fundamental form of the Bodhisattva. As can be seen he is spreading a half bloomed lotus, symbolizing the vow and ability to find purity amidst impurity, to open the Lotus of enlightenment in all our hearts.
Om tare tuttare ture svaha
This is the mantra of 绿度母 Green Tara, but as she is born from the left eye of Avalokitesvara and from his tears of compassion, she is regarded as his manifestation. She holds a blue lotus in the left hand, and her right hand forms the mudra of wish fulfillment. Her right leg is supported on a pink lotus. She is very popular in Tibet where she is reverently called the "Deliverance Mother" for her ability to fulfill wishes & lead sentient beings across the sea of samsara.
Om vajra dharma hrih
This is the heart mantra of 千手千眼观世音菩萨 Sahasra-bhuja Sahasra-netra Avalokitesvara, the Bodhisattva in his utmost majestic form, with a thousand eyes and arms. These eyes and arms represent the miraculous power of his all-seeing and all- embracing compassion. There are 3 versions of the main mantra, called the Dharani of Great Compassion, in Sanskrit, Tibetan and Chinese. I don't know which one is the most accurate, as they are all different in some way. One thing is for certain, though. It is one the greatest mantras taught to sentient beings, praised by all enlightened ones and recited in all worlds.
Om cale cule cundhe svaha
This is the heart mantra of 准提观音 Cundhi Avalokitevara, the Bodhisattva as the chief of all merits in the Lotus Court, a buddha-bhagavati (female buddha) deity. Reciting this heart mantra is equivalent to invoking the blessings of all Lotus deities. Cundhi means purity & calmness. She has 18 arms with various Dharma instruments, signifying her vast & limitless ability to save & benefit all sentient beings.