It goes something like this:
When we are holding by the bakoshas (the middle blessings) in the Shemoneh Esrei, by definition we are in asking mode, as in please give us wisdom, health, parnossa etc., in addition to forgive us, make nice vis à vis our personal problems, hear our prayers and seven other requests.
We make these petitions because it pains us to be without a livelihood or to endure our present exile. And not only are we permitted to do so, we are ordered to. Praying is not optional. The halacha is that we must petition Hashem three times a day (for men at least) by means of the Shemoneh Esrei with all of the intellectual and emotional energy that we can marshal.
That's what is expected of us and that's what most of us attempt to do, in theory at least. At room temperature, the story on the ground, as everyone knows, is somewhat different. We do the asking to be sure, but personal exceptions notwithstanding, more often than not our laundry list recitals don't quite hack it pain wise.
But truth be told, even if we did it right and put forth our requests with the requisite kavanah it would still be only second best.
So what's numero uno as to what our kavanah should be?
We should be focused on Hashem's pain, not ours, but Chazal well understood that if we couldn't get it together as to our own problems it was pointless to make it a requirement to focus on the pain that Hashem endures.
Meanwhile, it is well known that on Rosh Hashana we should have in mind with our tefillos to crown Hashem King of the whole world.
Rabbi Avraham Tzvi Schwartz lets us hear in the name of the Nefesh HaChaim that this should be our mindset every day. When a person davens he should have kavanah to crown Hashem King of the world. And, moreover, we should be davening for Hashem's needs.
He tells us that even when you are davening for your own needs that's also Hashem's needs because it helps remove the chilul Hashem that attaches to us if we don't have.
You're davening to be cured of some ailment, to have food on the table or for something else that you lack? It's a chilul Hashem for G-d's people to be sick or to lack anything in this world.
Our pain is Hashem's pain.
Yes, we're supposed to ask for our needs but what should really pain us is the pain that Hashem feels because they have not been met.