The basic idea is that God grants each of His people a certain level of authority over those nouns (people, places, things) which they mutually affect - one's body, family, home, relationships, workplace, etc. One is then empowered to powerfully intercede on behalf of those nouns; but if said someone doesn't fully acknowledge their spheres of influence and authority and then properly order them, it can be very difficult to remember and keep track of them.
So this has helped a lot. Also, some of the gems that Jon has dropped on us in the past couple sermons at TGC:
Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God. And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus.
To clasp the hands in prayer is the beginning of an uprising against the disorder of the world.
Now. This is all great and good, don't get me wrong - but it's not the sum total that I am after. If it was, then a 24/7 house of prayer and worship in NYC or Chicago would be sufficient. My heart and mind would be guarded by the peace of God and I might be on my way to uprising against the disorder of the world. My only problem with this (typical) understanding of prayer is that it falls just short of dispatching us. We are guarded, ready for the uprising... but just when does this uprising begin?!
I don't pretend to know the answers, though I have some ideas. Here's a satirical (though honest) poem I wrote today which might help to point us in the right direction:
I pray for peace in my life;
I'm always busy, hurried, anxious.
I pray for peace in my family;
I rarely call my mother.
I pray for peace in my relationships;
I hope to avoid confrontation.
I pray for peace in my home;
I hardly make the time to keep it.
I pray for peace in my building;
I've yet to meet my neighbors.
I pray for peace in my neighborhood;
I don't support local businesses.
I pray for peace in my city;
I refuse to confront the injustice in it.
I pray for peace in my country;
I prefer the cheap goods produced in others.
I pray for peace in my world;
I won't be the change I pray for.
Goddammit, He never answers my prayers.