Unfortunately one does not become a "grandparent" automatically when one's child has a child. The grandparent relationship, no matter how much one may desire it, is contingent upon the relationship that the grandparents have with their child (the mother or father of their grandchild) and their child's partner (the other parent of the child). It is the parents who determine how much time and what type of access the grandparent will have to the the grandchild. So it behooves every grandparent to establish and maintain a good relationship with their children and their children's spouses and to defer to the decisions of the grandchildren's parents no matter how much the grandparent may disagree with some of those decisions. (Aunt Josie is still learning in this area also.)
As with most relationships, communication with the parents is paramount. Refusing to criticize parenting decisions and not undermining or sabotaging parental actions is very important. Following directions and trying to stay available for babysitting and any other type of assistance that you can offer will also be helpful. Listening carefully to any objections that your grandchild's parents may have to your behavior without becoming defensive will go a long way too. Acknowledging that it has been a long time since you were a parent and that parenting methods may have changed gives your child lee-way to trust in your flexibility and ability to follow their directions.
Finally, remember that you are not the mother or father. Your loving role is secondary and supplemental to those of the parents. If you follow these "rules," With any luck, your children will allow you to enjoy their children and you will experience the joy that comes from establishing a relationship with that special little person.