I believe that when we say, "Thy kingdom come," we are both asking for His kingdom to be established on the earth as well as acknowledging that it will be so. Since we are constrained by time and space, for us this will hapen sometime in the future. However, I believe that this work, this establishment of His kingdom, has really already occurred; we just have not experienced it yet. I believe that God, the omnipotent, established His kingdom when Jesus cried out, "It is finished."
We ask for the Father's will because His will is true and perfect. We are humbling ourselves and bowing to His authority.
This prayer should affect our living by causing us to think, speak, and act in accordance with the Father's will, yielding to Him and supressing our earthly desires.