"ACTS" method of prayer

Adoration - Praising, worshipping God, for Who He is.
Confession - Asking God to cleanse us from sin.
Thanksgiving - Believing, acknowledging God's grace.
Supplication - Our specific prayer requests.

Adoration

Always begin prayer, by getting our heart, soul, mind, and strength fully focused on our Almighty and awesome GOD. 

Psalm 18:2

The Lord is my rock, my fortress and my deliverer;

my God is my rock, in whom I take refuge,

my shield and the horn of my salvation, my stronghold.

Focusing on God Himself, and our relationship to Him, we offer the Lord time to comfort us by His Holy Spirit, to convince us that He hears us, and that He is able and willing, to deal with the requests we would bring before Him 

Matthew 6:8

Do not be like them, for your Father knows what you need before you ask him.

Confession

Seek the Holy Spirit's conviction of sin, that we might ask God for forgiveness, and trust Him to cleanse us by the blood of Christ.

1 John 1:9

If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness. 

Psalm 139:23-24

Search me, God, and know my heart;

test me and know my anxious thoughts.

24 See if there is any offensive way in me,

and lead me in the way everlasting.

Thanksgiving

Acknowledging that all the blessings come from God alone, plus believing, and receiving these blessings. Put on the full armor of God" while thanking the Lord for all that He has already done for me in Christ.

Ephesians 6:10-18

The Armor of God

10 Finally, be strong in the Lord and in his mighty power. 11 Put on the full armor of God, so that you can take your stand against the devil’s schemes. 12 For our struggle is not against flesh and blood,but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms. 13 Therefore put on the full armor of God, so that when the day of evil comes, you may be able to stand your ground, and after you have done everything, to stand. 14 Stand firm then, with the belt of truth buckled around your waist, with the breastplate of righteousness in place, 15 and with your feet fitted with the readiness that comes from the gospel of peace. 16 In addition to all this, take up the shield of faith, with which you can extinguish all the flaming arrows of the evil one. 17 Take the helmet of salvation and the sword of the Spirit, which is the word of God.

18 And pray in the Spirit on all occasions with all kinds of prayers and requests. With this in mind, be alert and always keep on praying for all the Lord’s people.

Ephesians 1:3

Praise be to the God and Father of our Lord Jesus Christ, who has blessed us in the heavenly realms with every spiritual blessing in Christ.

Supplication

Pray within a state of full faith and awareness of God's work in Christ for us, that His Spirit would lead us into extraordinary victory in prayer. First thing, ask God to fill us with the overflowing of Holy Spirit in order to help us absolutely focus our complete attention on Him.

Luke 11:13

If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!

Now, make your requests known to God and express what's in your heart to Him. Notice that, once we are in God's presence, He begins to grant us faith to ask Him for greater things than we ordinarily would be inclined to ask. We have entered the presence of the One for Whom nothing is impossible, and suddenly, everything seems possible! and He begins to guide our prayer through His Holy Spirit.

The order of the ACTS method is crucial, for two reasons.

1. To make sure this experience of God's presence is purely Biblical, inspired by His Word, led by His Spirit,
2. Prayer should be God centered and by the guidance of His Holy Spirit should not be "self or need centered". We are the ones dependent on God's graces and not the other way around. Through the intercession of the Holy Spirit we pray to the God and not by commanding God what to do by our own will.