In Tana De'Vei Eliyahu: God said to Elijah,  the prophet, "I will let you know some of my traits. Sometimes you have people that have not a drop of Torah or good deeds in them, and yet when they turn to me and are involved very much in praying to me, then I pay attention to them, as it says in the verse 'He turns to the prayer of the empty one.'"

1.) Tana De'Vei Eliyahu  is one of the standard Midrashim. It has similar status and authority as the Midrash Raba and Tanchuma.

2.) The idea of "private conversation"is first that it is private. It is in a place where no one else is around. Also it is not from  any prayer book. It is ones own words that one says to God.

3.) I should mention that this is the only kind of prayer I feel has any  validity. The standard prayers I think are a waste of time. If one is learning Torah then he is not obligated in the standard prayers. That is a regular Halacha in the Rambam and Shulchan Aruch. If one is involved in learning a vocation the time that is most important is right when he gets up in the morning. To spend that time running to shul to half heatedly say words he does not mean and then to start his studies means he will not get very far. This is why in fact people that do this can't do anything well. This is because all their efforts and energy is not going into real prayer and not going into their work either.

4.)  prepare a pack lunch and go into the forest every day all day long to talk with God. I actually tried this for  a few years in Safed. I don't this anymore. But I still feel that when things are confusing for me that there is no other address to go to but to God directly.