There are many ways to read the Lord's Prayer, but one of the best ways of connecting the ideas in the prayer is seeing it from the perspective of a child. In explaining this idea, I will be quoting the prayer from a literal English translation from the Greek.
The Family of the Divine
The prayer stars with "our Father." (See this article on the Greek of the first line.) Why is the Father "in the skies?" From the perspective of a child, all fathers are seen against the background of the sky because the child must look up to them.
The next line in the common translation is "hallowed be thy name." Again, this line can be understood as a child being taught the importance of the family name. All families survive based on the good name of the father.
The Realm of the Divine
The two lines, "thy kingdom come, thy will be done" and not very accurately translated in the popular versions of the Bible (see the article here). The Greek is a more interesting than the English translation but unnecessary for the point of this article. What is the realm of a father when compared to the realm of a child? Fathers live in a bigger universe than their children. Children do not understand that larger world of adults any more than we understand the realm of the Divine.
So what is a father's will or desire for his children? That they should grow up and see the larger world as it is. The higher, bigger, more valuable realities of the universe should be revealed to us and begin to shape our earthly lives.
The Dinner Table
The prayer then moves to the most basic scene of family life: the dinner table. (See this article on the Greek.) is is where we ask our father for the nourishment we need to survive. The Greek word translated as "daily" actually means "that we exist upon," which implies not only earthly bread, but the nourishment that we need that goes beyond bread alone.
The dinner table is not only about food, but about discussing what has gone wrong during the day. In the Lord's prayer, this discussion turns toward our debts, shortcomings, and the conflicts among the children. (See this article.) The Father forgives us ours mistakes, but only we forgive our siblings their mistakes in return.
Depending how we are able to resolve these debts, one of two possible resolutions of our shortcomings is possible after dinner. (See this article.) A father doesn't want to take any of his children to the woodshed, but he may have to. The more desirable choice, however, is pulling his children toward him in a hug, taking them out of their foolishness.
This is exactly what the last two lines say in a literal translation: "Also, you might not want to bring us as far as a trial. Instead, draw us toward Yourself away from what is worthless."
So the prayer is a perfect picture of a father: someone we look up to, the protector of the family name, the ruler of a large universe, who seek to teach us the rules of that universe, a breadwinner, a forgiver of wrong, an enforcer of reconcilation among family members, and, ultimately, the source of correction and hugs.