"That is, the way (and the what) that one prays is intimately and reciprocally related to the way (and the what) that one believes."
It is a simple fact that "out of the overflow of the heart the mouth speaks" (Matt. 12:34; Lk. 6:45). And it is reasonable to extrapolate from that that our understanding of our Christian faith will come out in prayer.
This, if anything, should give us impetus to "go into your room, close the door and pray to your Father, who is unseen" (Matt. 6:6). For it is there, in your room, in prayer, that your real education will begin (Dostoevsky, Have Mercy On Those Who Come Before Thee). It is there that what you believe will be meted out under the beneficient guidance of the Holy Spirit. It is there that you will "continue to work out your salvation with fear and trembling" (Phil. 2:12). It is there that the soul stands taller when the body is on its knees.
If the 'law of prayer is the law of believing', then what an amazing opportunity we have to step into the Holy of Holies and ask God what it is we should believe, how we should go about practicing it, and how we can articulate it in ways that help others (1 Pt. 3:15-16)! If what is prayed is what is believed then each of us has a duty to listen that much more closely to the prayers of our brothers and sisters so that we can learn from their life with God, and gently correct if what they pray is not what they practice. At the same time, we are wise to receive admonitions from our brothers and sisters if what they hear us praying is not what they see us practicing.
So what is it that we can be confident about believing? There has to be some baseline, some suppositional starting point where we throw ourselves into the mix and try and figure out what is right to believe. And the primary answer to that is, the Word of God.
Our prayers should be steeped in the Word of God, drawing on His words to inform our hearts, minds, and bodies. We are to let the Word of God indwell us, take up home in us, live in us (Col. 3:16-17), and by doing so, "whatever [we] do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to God the Father through Him."
It is a linear application: the Word of God prompts its own expectations. That is, because the Word of God is living and active (Heb. 4:12), and indwells the believer, it urges what it teaches; it spurs the believer on to what it declares. In that sense,
"...doctrine informs practice, but practice in turn shapes doctrine. What the church does, and how she does it, not only confesses but in time also determines what she believes and teaches. The practice of prayer is a way of teaching; indeed, it is a primary means of catechesis, which forms thinking and believing."
The living Word of God that indwells each Christian is the baseline for all Christian belief. What God has said, we believe; what we believe should be what we practice. Hence there is a direct correlation between what a Christian prays who has the living Word of God indwelling him, and what he practices. And what should the Christian practice? Matthew 25:31-46 and James 1:27 give clear, though not exhaustive answers to that question.
The secondary answer to what is right to believe comes down to us through the "democracy of the dead" (G.K. Chesterton). That is, through the creeds (Apostle's, Nicene, and Athanasian) and traditions of believers who have gone before us. The creeds (from the Latin credo, "I believe") summarize the heart of the Christian faith by placing the chief doctrines of Scripture in brief.
Looking to the freedom of the saints of the past points us to the freedom we can enjoy in Christ both now, and in the future. Their exemplary lives serve as a constant guide for how 'the law of prayer is the law of belief' by highlighting the intersection between what they believed and how they practiced it.
We do well to heighten our attention to our prayer lives. Prayer is our umbilical chord to God. It is how we are fed, because in prayer God reinforces His Word so that it indwells us. From there, what we pray forms what we believe, and what we believe becomes our practice. Rev. Stuckwisch can have the last word on this subject:
"So we are rightly concerned with "prayer," broadly speaking, as a teaching and confessing of belief. Right praying serves, supports and substantiates right believing, in much the same way that heterodox praying is both indicative and precipitant of heterodox believing. That's basically the affirmation and the warning implicit in "lex orandi, lex credendi," as it is typically summoned to duty."