I was always taught that to remember prayer, we should remember ACTS. It's a good way of modelling our prayer.
Adoration - we always come to God remembering that He is sovereign, holy, all knowledgeable and all powerful. He is worthy of our praise (Psalms 145:3).
Confession - we come to God acknowledging our sins and receiving his forgiveness (1 John 1:9)
Thanksgiving - we thank God for the good things He has done in our lives, for his faithfulness and his provision for us. Only one of the ten lepers who were healed came back to thank Jesus (Luke 17:11-19).
Supplication - we come to our God with our requests. Supplication comes from the latin supplicare which means to "plead humbly". We should continue faithfully with our prayers such as in the parable of the persistent window in Luke 18:1-8.