We find one approach to meaningful prayer described in the Mishnah:
"The early Hasidim would set aside an hour and then pray, so that they would turn their hearts to God."
This path is of an extremely individual nature.
Here, a person comes to terms with the truth of himself.
He attempts to reach, within himself, the ideal of perfection.
Since it is very difficult–indeed, almost impossible–to explain and describe such a thing to another, this path is shrouded in mystery.
It is a path upon which few proceed.
This preparation is not accomplished by studying or meditating upon some topic, but by aligning one's mind and heart, of clarifying one's personal experience, of extracting truth as it pertains to oneself.
R. Leibele Eiger asked the Kotzker Rebbe what to tell his noted grandfather, R. Akiva Eiger, when the latter would question the Hasidic custom of delaying one's prayers.
The Rebbe replied that this is a halachah to be found in Maimonides' writings.
If a worker is hired to chop down trees and he spends most of the day sharpening his axe, he gets paid in full.
It is possible to chop down trees with a dull ax–or, for that matter, with a piece of flint–but the work will require tremendous effort, will take a great deal of time, and the outcome will be unsatisfactory.
But when the tool is sharpened, the work can be completed quickly.
This way of preparation for prayer is the same: a person directs himself, sharpens his sense of the presence of God so that it becomes real, and only then does he pray.
We may say that all of the work–besides the prayer service itself–is incorporated into the preparation.
All of the work of directing and focusing oneself have already reached full expression before the prayer service has begun, and so during the prayer service there is no need to pray at length.
From the pinnacle of truth a person has already attained, his prayer streams spontaneously.
–Rabbi Adin Steinsaltz
From "Prayer," in The Thirteen Petalled Rose (new edition) by Rabbi Adin Steinsaltz