OK, get Matthew chapter 6, where that expression occurs, and I'll give you an example in Daniel 9Matthew 6 in one hand, and Daniel 9 in the other.
Now some of the new bibles have changed this vain repetition to something else.  One of them says, "Babbling," and one of them says, "Useless," something or other.
So the question is, How can you pray about one thing for a long period of time without vain repetition?
All right, Matthew 6:7:  "But when ye pray, use not vain repetitions, as the heathen do:  for they think that they shall be heard for their much speaking." Now, vain repetition there cannot mean just repeating.  It's VAIN repeating.  Vain repetition.
And I'll show you in a minute, from the model prayer, that it can't mean just repeating, because one of the greatest prayers in the Bible is repetition throughout.  And, what He is condemning in Matthew 6:7 is this business about, "Our Father which art in heaven, hallowed by thy name, thy kingdom come," etc., etc.--and flip the beads around.  "Our Father which art in heaven, hail, Mary, Mother of God, full of grace, Lord," that business.  THAT's vain repetition.  That's saying one prayer over and over and over and over and over VAINLY.
Now, just to repeat a thing?  That isn't it.  For example, turn to Daniel 9, and notice this great prayer of repentance, how the same thing is repeated over and over again, and the Lord's name is repeated over again.  Daniel 9:3:  "And I set my face unto the Lord God, to seek by prayer and supplications, with fasting, and sackcloth, and ashes:  And I prayed unto the Lord my God, and made my confession, and said, O Lord,..."
Verse 7:  "O Lord,..."
Verse 8:  "O Lord,..."
Verse 16:  "O Lord,..."
Verse 18:  "O my God,..."
Verse 19:  "O Lord,..."
"O Lord." "O Lord." "O Lord." "O my God." See?  That doesn't come under the heading of "vain repetition" there.
As a matter of fact, real praying finally reduces itself to about three words.  From what I know about men and about people, I find that when a man gets really desperate, he's praying, "O my God!" And you watch the guy get hurt on a job, by accident, or out there in a car wreck.  Or a guy under shell fire or artillery fire:  "O my God!  O my God!  O my God!", you know.  And then it's reduced to, "O God!" It comes down finally, if the guy isn't saved especially, he doesn't say, "O my God!" He says, "O God!  O God!  O God!", you know.
Boy, if you had a dollar for every time those two words were said in combat, you'd be rich.  An atheist out there saying, "O God!  O God!"
And when you get rid of that, you're down to, "Oh!" And it finally reduces to that.  It comes to "O my God!" And then "O God!" And then just "Oh!  Oh!  Oh!" Down to that.
And, when those things are said from the heart, under burden, that's not vain repetition.
Now, look at Daniel's prayer again, and look at the subject matter here.  Verse 5:  "We have sinned, and have committed iniquity, and have done wickedly, and have rebelled." Verse 10:  "Neither have we obeyed." Verse 11:  "Transgressed," "Departed." See that business?  That whole thing is just a confession of sin!  But God doesn't count that vain repetition.
Now, there's progression, if you wait on the Lord.  Let's come to Matthew for a minute.  And, if you find yourself praying about one thing, just over and over again, in one prayer at one time, you're not waiting enough between the petitions to see what the Lord is doing with it.  For example, come to Matthew chapter 26.  And in Matthew 26, look at the progression in this prayer.  And Christ is only praying about one thing.  Matthew 26:39:  "And he went a little farther, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me:  nevertheless not as I will, but as thou wilt." Verse 42:  "O my Father, if this cup may not pass away from me, except I drink it, thy will be done." Verse 44:  "The third time, saying the same words." Now that's the greatest prayer in the Bible; that's Gethsemane.  That's blood, sweat, and tears.  And the content of that prayer is not even thirty words--not even thirty words.  But there are gaps in there.
And, if you ever prayed for somebody to get well who was dying, if you ever prayed for a sick boy or girl or something like that, and you've been along there, it's the place where you get down there and you pray, and then you wait.  And then you beg again, and then you cry awhile.  And then you quit crying, and nothing happens.  And then you wait, and you start in again.  And then finally you're all prayed out, and can't think of anything else to pray.  And you just wait awhile.
I've had prayer meetings at times when I was afraid to look up when I got through praying.  Any of you been like that?  I mean, it wasn't that anybody was standing there.  I mean, I don't believe in spooks or anything.  But, I'll tell you, man, there's a Presence there.  There's a Presence there.  There've been times, when I got through praying, and thought I'd prayed the thing out, where the Lord just said, "Just keep your head down a little bit longer."
And so I'd say this:  I'd say, I wouldn't worry about a vain repetition where you're sincere.  But if you're just saying the same words over and over again like a wheel, then just stop and wait, and watch the Lord begin to work.
You know, many times He begins to work on us.  You ever get that?  I mean, "Lord, get me a new car.  Lord, get me a new car.  Lord, get me a new car." And then there's a blank.
And the Lord says, "Oh, by the way, if I get you a new car, do you remember what you did with that last one?"
And you mumble, "Yeah." And go on, "Lord, get me a new car.  Get me a new car!"
And then there's a blank, and the Lord says, "If I get you a new car, will you pick up some folks and take them to church?"
"Oh, yeah, yeah, sure, sure!" Then you pray again for awhile, you know, and there's a big blank.
And the Lord says, "Well, now, if I get you a new car, will it interfere with your missionary offering?"
"Well, you know, Lord, it's been kind of hard, and I've been laid off, you know, and I got a lot of bills I've got to get out of the way first."
See, that's how prayer goes.  When you get down to pray and tangle with the Lord, you just don't run in there, you know, and press the button and say, "Hello, bell boy, give me a pitcher of ice water." You wait awhile and let the Lord deal with you.