On the Energizing Your Prayers page, there is a discussion on how to supercharge your prayers with humility, almsgiving, and fasting. Those are all very positive things which will definitely help your prayers be heard in heaven. However, before that, there are some negative things that must be removed from your life first. This is directly analogous to pulling up the weeds in your garden before you plant your garden and fertilize it. There are very firm rules for loving relationships. For instance, no husband can have a great relationship with his wife if he is committing adultery at the same time. No father can have a great relationship with his children if he cusses them out all the time and beats them. Just so, if you want a great relationship with Jesus, there are certain things that you cannot do, like breaking any of the 10 Commandments, not loving your neighbor (including those you really don't like), not going to Mass, etc.
Very few people, if any, do all of the things below, but the more that you do, the more likely your prayers will be heard. And always remember to pray from the heart, with all humility and forgiveness for everyone. Remember, God is your loving Father who will always take care of you, not some kind of military commander taking orders from his subordinates!
1. Never pray for something without first asking for increased faith.
Hebrews 11:6: And without faith it is impossible to please him. For whoever would draw near to God must believe that he exists and that he rewards those who seek him.
2. Never pray with any DOUBT.
Mark 11:22-24: And Jesus answered them, "Have faith in God. Truly, I say to you, whoever says to this mountain, `Be taken up and cast into the sea,' and does not doubt in his heart, but believes that what he says will come to pass, it will be done for him. Therefore I tell you, whatever you ask in prayer, believe that you have received it, and it will be yours.
James 1:6-8: But let him ask in faith, with no doubting, for he who doubts is like a wave of the sea that is driven and tossed by the wind. For that person must not suppose that a double-minded man, unstable in all his ways, will receive anything from the Lord.
Matthew 6:14-15: For if you forgive men their trespasses, your heavenly Father also will forgive you; but if you do not forgive men their trespasses, neither will your Father forgive your trespasses
Psalm 37:4: Take delight in the LORD, and he will give you the desires of your heart.
In the Lord's prayer, "Hallowed be thy Name" comes before "give us this day".
1 John 3:22: and we receive from him whatever we ask, because we keep his commandments and do what pleases him.
Psalm 66:18:If I had cherished iniquity in my heart, the Lord would not have listened.
Jeremiah 29:11-13: For I know the plans I have for you, says the LORD, plans for welfare and not for evil, to give you a future and a hope. Then you will call upon me and come and pray to me, and I will hear you. You will seek me and find me; when you seek me with all your heart.
1 Peter 3:7: Likewise you husbands, live considerately with your wives, bestowing honor on the woman as the weaker sex, since you are joint heirs of the grace of life, in order that your prayers may not be hindered.
Luke 18:1-8:And he told them a parable, to the effect that they ought always to pray and not lose heart. He said, "In a certain city there was a judge who neither feared God nor regarded man; and there was a widow in that city who kept coming to him and saying, `Vindicate me against my adversary.' For a while he refused; but afterward he said to himself, `Though I neither fear God nor regard man, yet because this widow bothers me, I will vindicate her, or she will wear me out by her continual coming.'" And the Lord said, "Hear what the unrighteous judge says. And will not God vindicate his elect, who cry to him day and night? Will he delay long over them? I tell you, he will vindicate them speedily. Nevertheless, when the Son of man comes, will he find faith on earth?"
Deuteronomy 18:10-12: There shall not be found among you any one who burns his son or his daughter as an offering, any one who practices divination, a soothsayer, or an augur, or a sorcerer, or a charmer, or a medium, or a wizard, or a necromancer. For whoever does these things is an abomination to the LORD; and because of these abominable practices the LORD your God is driving them out before you.
James 4:2-3: You desire and do not have; so you kill. And you covet and cannot obtain; so you fight and wage war. You do not have, because you do not ask. You ask and do not receive, because you ask wrongly, to spend it on your passions.
John 15:7:If you abide in me, and my words abide in you, ask whatever you will, and it shall be done for you.John 6:56:He who eats my flesh and drinks my blood abides in me, and I in him.
1 Corinthians 11:27-30: Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. Let a man examine himself, and so eat of the bread and drink of the cup. For any one who eats and drinks without discerning the body eats and drinks judgment upon himself. That is why many of you are weak and ill, and some have died.
John 16:23: In that day you will ask nothing of me. Truly, truly, I say to you, if you ask anything of the Father, he will give it to you in my name.
Luke 18:9-14: He also told this parable to some who trusted in themselves that they were righteous and despised others: "Two men went up into the temple to pray, one a Pharisee and the other a tax collector. The Pharisee stood and prayed thus with himself, `God, I thank thee that I am not like other men, extortioners, unjust, adulterers, or even like this tax collector. I fast twice a week, I give tithes of all that I get.' But the tax collector, standing far off, would not even lift up his eyes to heaven, but beat his breast, saying, `God, be merciful to me a sinner!' I tell you, this man went down to his house justified rather than the other; for every one who exalts himself will be humbled, but he who humbles himself will be exalted."
Matthew 18:19-20: Again I say to you, if two of you agree on earth about anything they ask, it will be done for them by my Father in heaven. For where two or three are gathered in my name, there am I in the midst of them."James 5:16: Therefore confess your sins to one another, and pray for one another, that you may be healed. The prayer of a righteous man has great power in its effects.
Sirach 3:5: Whoever honors his father will be gladdened by his own children, and when he prays he will be heard.
Luke 10:16: "He who hears you hears me, and he who rejects you rejects me, and he who rejects me rejects him who sent me."Matthew 18:17: If he refuses to listen to them, tell it to the church; and if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector.
Proverbs 3:5: "Trust in the Lord with all your heart, and lean not on your own understanding; in all your ways acknowledge Him, and He shall direct your paths."
Sirach 2:6,8,10,13: Trust in him, and he will help you; make your ways straight, and hope in him. You who fear the Lord, trust in him, and your reward will not fail; Consider the ancient generations and see: who ever trusted in the Lord and was put to shame? Or who ever persevered in the fear of the Lord and was forsaken? Or who ever called upon him and was overlooked? Woe to the faint heart, for it has no trust! Therefore it will not be sheltered.
Sirach 11:21: Do not wonder at the works of a sinner, but trust in the Lord and keep at your toil; for it is easy in the sight of the Lord to enrich a poor man quickly and suddenly.
John 9:31: We know that God does not listen to sinners, but if any one is a worshiper of God and does his will, God listens to him.
22. Do not live according to the flesh.
Romans 8:7-8: For the mind that is set on the flesh is hostile to God; it does not submit to God's law, indeed it cannot; and those who are in the flesh cannot please God.