A genuine Christian experience in prayer is to come to the edge of the road and to recognize uncharted territory and not know the way — but, instead of turning back, cutting our way through the thickets and dense grasses in faith through the power of the Spirit. That, I think, is what Romans 8:26-27 speaks of when it speaks of the Spirit interceding on our behalf. Paul defines prayer here brilliantly, and it unlocks much of what we need to learn about prayer.

The Spirit helps us in our interecessions because we do not know how to pray — the Spirit’s intercessions takes the form of “sighs too deep for words” because God, “who searches the heart” knows the “mind of the Spirit” — and the Spirit intercedes in light of the will of God.
There is a lot here, and even some controversies. (Wright doesn’t think this is about tongues, just in case you’re wondering.)
What the Christian is praying for is redemption of the whole order — a yearning and longing for God’s future to be brought forward or for the present to be swallowed into God’s grand plan. It is not that we hand on our requests to the Spirit but that the Spirit, in a sense, takes over our longings and, because the Spirit knows God’s will, carries us along to what we can’t articulate.
God is here described, acc. to Wright’s nice phrase, as the “heart-searcher”.
Nothing less than this is being said: genuine prayer is being caught up by the Spirit into the redemptive will of God. I suggest we see that genuine prayer as the Lord’s Prayer itself.