Saints don't come from a cookie-cutter mold. Some attain this status by virtuous living and others for surrendering to a brave and holy death. Some were saint-like from childhood (see the lives of Prince Casimir of Poland, Catherine of Siena, or Maria Goretti). Others were knaves for quite a while first (check out Augustine, Pope Callistus I, and Bernard of Corleone).
Technically, you make the register of saints by undergoing a process known as canonization, which includes a thorough examination of the life and circumstances of the person under consideration. Dying for the faith (martyrdom) is the quickest route into the canon of saints, and posthumous miracles credited to your intercession always help, though they've not always been strictly necessary.
But for every saint who makes the official canon there are thousands and thousands of holy people who fly under the radar of each generation, living and dying in equally astonishing measures of grace. What it comes down to is that canonized saints are held up as examples of virtuous living for the whole church, but the saints of God are more numerous still.
So does that mean you can pray to your kindly departed grandmother? That depends on a sound understanding of how we interact with saints of any kind. Despite what you may have seen or heard, Catholics don't worship saints. Worship and adoration are reserved for God alone in the Persons of the Trinity. What we offer saints is veneration: due honors for their achievements in grace. (Mary, the Mother of God, gets a higher veneration called hyperdulia, but even she is not a candidate for worship.)
We also seek the intercession of saints: their spiritual assistance. Saint Dominic consoled his brothers at his death by reminding them: "Do not weep, for I shall be more useful to you after my death and I shall help you then more effectively than during my life." If your grandmother were a holy woman in life, she'd probably agree with Saint Thérèse of Lisieux, who declared: "I want to spend my heaven in doing good on earth."
Matthew 5:1-12; 16:24-25; 2 Corinthians 13:11-12; Ephesians 1
Saint of the Day
Sister Wendy's Book of Saints by Wendy Beckett (Loyola Press, 1998)
Holy Simplicity: The Little Way of Mother Teresa, Dorothy Day, and Thérèse of Lisieux by Joel Schorn (Servant Books, 2008)
God's Doorkeepers: Padre Pio, Solanus Casey, and André Bessette by Joel Schorn (Servant Books, 2006)