The name of your Catholic church: check your parish website to see if it provides some background its saint. Maybe there is an icon or statue of the saint.
Your family’s heritage: Celtic saints like Saint David of Wales have a unique history of wandering around in boats without oars or connecting with nature. Italian saints represent a tremendous heritage: Saint Francis, Saint Clare, Saint Catherine of Siena are just a few. If you are German, Saint Hildegard of Bingen was a truly gifted saint who wrote plays and songs. Latin American and South American saints like Mexican Saint Juan Diego, a model of faith, and Peruvian Saint Martin de Porres, a model of service, are inspirations.
Sense of place: Perhaps there is a place where you’ve traveled where you’ve felt a sense of connection where a saint also lived. Maybe you’ve visited a church dedicated to a particular saint. Pay attention to the call of the Holy Spirit in places like these.
Hobby or Job: Saints are often the patrons of everyday activities like baking, fishing, etc. If you enjoy these, connect with the related saint, just as you would with a typical friend. For a list of patrons, see http://www.catholic.org/saints/patron.php
Animals: Kids especially enjoy stories of saints helping, or getting advice from, animals. In one story, St. Patrick refused to let his companions hunt a deer and her fawn, because they rested on a hilltop site where he wished to build a church. Catholic Icing has compiled a wonderful list of saints and their animals; see http://www.catholicicing.com/animals-for-peg-dolls/
Prayer: A way of praying from a certain saint may touch your soul. When I was first considering becoming Catholic, I struggled to move beyond my childhood perceptions of God as a punishing “judge.” When I heard the Breastplate of St. Patrick prayer, “Jesus with me, Jesus before me, Jesus behind me, Jesus in me, Jesus beneath me…,” I began to change, knowing Jesus wanted to enfold me in love, hope, and protection.
St. Patrick became a guide and friend. I wish you luck in finding a saint friend as well!