The Lord's Prayer, when we pray it either as Jesus gave to us or as a template, where we use the ideas in it to formulate our own prayers with, teaches us to trust God and depend upon him more. There are six "petitions" in it. Each petition teaches us something about God and draws us closer to him when we pray it.
The prayer begins with God, specifically with how to address God. Jesus teaches us to call God "Father." God is the one who cares for us and provides for us as a Father. The rest of the prayer is understood in this context--as the Father's loving provision for his children.
The second petition teaches us to honor and glorify God's name by praying that his name would be hallowed. As children who love our Father, we want his name to be magnified in the world and this petition causes us to pray about how that might happen.
Linked closely to this is a prayer that God's kingdom, his work in the world, would be brought to completion. As we pray about this, we realize that as his children, we work in his kingdom to help bring about his reign.
The fourth petition acknowledges that we depend upon our Father for our daily needs. We do not ask for what we want, or for a month's worth of provisions, so that we end up forgetting about God. Rather, we live day by day, trusting him and depending upon him.
The fifth petition reminds us that we live in a community of people who look to and love God as Father. As we seek to draw closer to God and we pray for forgiveness, God teaches us that we must also extend the forgiveness that we desire from him to our relationships with others. Forgiveness must be mutual.
Finally, the last petition encourages us to plead to God for help, specifically, to avoid temptation, to be kept from it, so we will be able to carry out his will.
The Lord's Prayer is a prayer of trust. As you pray it, either as it is or as a template, learn to trust God and depend upon him more.