What does the Bible say about how we should pray? Context

In Matthew 6:7-15, we see Jesus


telling his disciples to not use vain repetitions as the heathens do
giving a specific example of how to pray


It's furthermore noted that prayer is a rather powerful technique given:


Jesus prayed right before his death Luke 22:39-46
some demons can only be removed via prayer Mark 9:29


I get the impression that prayer is something that:


was very important to Christ and his disciples
unfortunately, for some reason, not explained explicitly in the Bible (i.e. no 8-step prayer program)


There are other Biblical truths that are "hidden" -- like Trinity / TULIP -- they're in the Bible, but often times hard to see unless someone shows it to you. Prayer seems to be along these lines.

Question

Who were the most influential Church fathers on how we should pray? And what did they say about it? [Please cite resources.]
The subject of prayer during the reformation also took on a revised meaning.  The reference I think best illustrates this is John Owen’s Works Volume 4 - ‘A Discourse of The Work of The Holy Spirit in Prayer; With a Brief Inquiry into the Nature and Use of Mental Prayer and Forms.’
In this work Owen makes several key concepts, which to me, represent the ‘reformed view’ of prayer and opposed some previous traditional views that were seen as apostasy from the biblical view. The traditional views being rejected by Owen were any view that pretended of some ‘secret steps’ to prayer as possibly proposed by monkish institutions or ‘prayer books’ that sought to replace the personal need of prayer according to ones own peculiar situation.
In this work Owen argues the following basic tenants.
First Owen uses a prophecy in Zechariah to stress that prayer is a general work of the Holy Spirit in all believers. Not only so but it is a primary function of the Spirit in our lives and hence of our faith itself.

And I will pour out on the house of David and the inhabitants of Jerusalem a spirit of grace and supplication. (NIV Zechariah 12:10)

He further establishes the root of his argument here:

Because you are his sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, “Abba, Father.” (NIV Galatians 4:6)
In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express. (NIV Romans 8:26)

To reduce his many words into a summary, this lays the foundation of the reformed view, for basically as the Spirit is the Spirit of the ‘Son’ and of ‘supplication’, prayer is what binds us into communion with God by faith in Christ whereby we learn what to pray and how to pray and are enabled to do so with a Christ centered faith and power.
First of all without the Spirit we do not know what to pray.  Inwardly the Spirit desires that we conform to the image of Christ by faith, but we are not even aware of our own sins or needs, without the Spirit groaning for our deliverance with in us and manifesting our needs to us.
Secondly, the Spirit makes know to us how the atonement and work of Christ is able to provide an answer to what we need. As we learn what our needs are and bring them to God and the study of his word, the Spirit by faith in Christ opens up his word and assures us in particulars, according to our private needs, what God’s will is and that he is able to supply all our needs accordingly.
Third, the Spirit makes us feel as God’s children with ‘bold-free access’ to God. Children trust that their parents will help them and so frequently approach them with all their requests over and over. Often it is ‘hidden guilt’ that keeps us from coming to the throne of grace boldly, which explains our atheistic prayer-less life. This is actually unbelief and I have made a very very long post against the work of guilt and fear in our secret hearts here and is related to our desire to approach God by prayer.  With guilt we may be compelled to the duty of prayer but will never know what it is to pray in the Spirit, for that work will be a work of the flesh.
The end result of a reformed view of prayer is that it is entirely connected to our relationship with God.  Prayer takes the gospel, digests it and expresses the desire for God’s will and kingdom in our lives, in the desire, love and earnest seeking of his will for ourselves and our neighbors – it is our 'faith-pulse' even if we are barely ware of it.
The result of prayer, therefore, is that our whole state of faith depends on it, and if our faith is weak, we need quite time with God to strengthen it in order to do the more difficult matters such as the reference made to casting out a powerful demon, which the Apostles who were at the time weak in faith, we not able to do. This type of prayer, though extending into verbal public prayers as occasions will require, cannot be replaced by any supposed ‘secret method’, or published ‘prayer book’ but is the most intense, intimate and personal aspect of our relationship with God and his word.  Some of the best types of prayers, as illustrative examples, are those offered by the Apostle in some of his epistles.