The Lord's Prayer is something that I learned when I was a wee kid, I've heard hundreds of times, and sat through a dozen sermons on, but I have never really studied it out for myself. Although I've always known that it was so, I was amazed at how much more there was then just a poem to repeat. I'm sure none of this is new, but I feel like it is what the Lord wanted me to share, so I'll try to scrape the top of this iceberg of learning.
Recognize God's holiness
"Our Father which art in heaven, Hallowed be thy name."
This is an oft overlooked step in my prayer life. I have always seen this as the intro to a prayer; approaching God with respect when we pray, but I think it means a bit more. It means acknowledging that God is infinitely more than me. When I place myself utterly beneath God, it creates a reliance of God, and helps me find faith in God. This may seem like an obvious thing, I was surprised at the perspective change, when I started applying this in my life; the things that seemed monumental to me, now look tiny in the hands of the creator of the universe.
Rest in God's will
"Thy kingdom come. Thy will be done, as in heaven, so in earth."
This is a prayer that must permeate every part of my prayer and life. It's not just part of a prayer (although it can be that, too); it is the core of everything I ask. When I don't preface my requests with seeking God's will, I will almost always be disappointed with the outcome, and be unhappy with God, for not giving me my will. As I seek God's will, and he makes it my desire, I find every other need does not matter to me at all, and I all that matters is whether or not God is glorified through my life.
Request provision
"Give us day by day our daily bread."
This is the proverbial bread and butter of the modern Christians prayer. This is the part that comes naturally to anybody that thinks there may be a God in Heaven. Provision encompasses everything from providing food, to providing knowledge, to providing direction.
Most of my prayer on a daily basis falls into this category (followed closely by the next category), but it is the humility from step one, and the faith from step two that give us the perspective to ask for what God wants us to have. How often I go to the Lord in prayer, and ask for something that I would never have considered, had I truly wanted God's will in my life.
Also, Jesus did not say "give us this day enough bread to provide for my family and keep this ministry going and to give me security and peace", he said "daily bread". Don't think that just because you can see a need in the future, and don't have the means to deal with it that God is not providing; he may be waiting 'til a time when he will receive the glory for meeting the need, or he may be teaching patience, or maybe he wants you to see that the "need" is really a "want". The point is (to both me, and whoever reads), that we should not go whining to God for months on end about everything, but rather seek his face about it, do your part of being a steward of this life, and trust him to take care of it. :)
Repent of our sins
"And forgive us our sins; for we also forgive every one that is indebted to us."
No matter how good life is going, how many hours I am spending in the Bible each day, how many people I have reached with the Gospel, I can always find something to confess to God. The times that it seems I can't, I am usually displaying pride, and self-righteousness. We all have the old flesh with which to deal, and each time we pray ought to be a time of self-examination.
Realize his grace
"lead us not into temptation; but deliver us from evil."
Where sin abounds, Grace does much more abound. God does not allow us to be tempted above that we are able. He has made a way of escape. All that we have to do is ask, and he will pour out his grace for situations we don't even know exist yet. You may have heard that "it's easier to ask for forgiveness than permission" before, but believe me, it is much much easier to ask for protection than forgiveness.
Notes: this is not a magic formula for reaching God's emergency phone line; it is simply what I see as elements of what God's wants when we pray. :) I know I may have stretched the headings a little, but I was enjoying alliterating. I don't think these are set in any particular order.