The festival begins tonight at 7pm, when there is a mass at San Matias church nearby and the statue of the virgin is lowered into the little cave. Most of the festivities are in the evenings and tourists can mingle with local people to celebrate this fiesta.
Here is some information about Artenara: http://www.canario.co.uk/artenara.htm
The place is near Tamadaba, the pine forest, and you can check the bus timetable for the number 18 bus here: http://www.globalsu.net/es/lineas.php
Alternately you can rent a car in Gran Canaria and explore the whole island on your holiday.