What does it mean to "Not pray as the Pagans do"?

This question arises when a believer is wanting to pray rightly and according to the patter given in Scripture. 

The Lord's Prayer example is given to us in 

Matthew 6:9-13 and Luke 11:1-4

Here is a basic study on the topic

Jesus pattern for every prayer 

This study answers the question about how did pagans pray, so we can avoid vain and worthless prayer today. (From this series).

Here are 8 messages on The Lord's Prayer:

Part 1  (scroll down) 

Part 2  (begins at the top)

Here are 12 messages on Matthew 6:9-13 you can use to study this pprtion of Scripture

And 11 here for Luke 11:1-4 and 2 more here to complete the prayer series.