You have asked a very good and timeless question. I will try to answer in a way that respects your honest desire as well as it reverences our Father in Heaven.
First, understand who you are praying to. Almighty God is your Father in Heaven. Even more than a good mortal father, He loves you and knows you.
To paraphrase a quote I once heard: He knows you as well as if you were His only creation, and He spent all His time with only you. He loves you as much as if you were His only child. He hears your prayers just as well as if He had nothing else to do but listen to you.
In the Bible, Jesus Christ taught both directly and by example how we should pray to the Father. The book of Matthew, chapter 6 has some particularly good instruction from the Master (My comments in italics):
Matthew 65 ...And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward.
We are to pray to the Father, for Him to hear, not to impress anyone else
6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
The Father knows you and loves you more than you can imagine. He knows everything you do and think and, perhaps most importantly in this case, everything you feel and experience. He knows your frustration and pain.
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.
When we pray, it must be real. He is not impressed by flowery words and expressions, but wants to hear it straight from our hearts. However, we need to still be respectful and reverent, not lashing out in anger or anything of that sort.
8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.
Again, he knows you and your circumstances very, very well.
9 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.
Note, Jesus teaches that we should pray "after this manner." He is giving a sample prayer, containing principles and elements which we should emulate. He did not tell us to necessarily repeat the exact words He uses. To begin with, the Son begins by addressing His Father and expresses reverent worship to Him.
10 Thy kingdom come. Thy will be done in earth, as it is in heaven.
We should follow the Savior's example by submitting to the will of the Father, rather than demanding that our will be done. This sometimes requires a great deal of faith and trust that the Father loves and cares for you personally.
11 Give us this day our daily bread.
We should pray for our needs to be met
12 And forgive us our debts, as we forgive our debtors.
...and forgiveness, which is tied to how we forgive
13 And lead us not into temptation, but deliver us from evil: For thine is the kingdom, and the power, and the glory, for ever. Amen.
...and protection from temptation and evil. All glory and credit belong to Him, for all good comes from Him.
So, a large part of prayer is approaching the Father with the right attitude. The right attitude is honesty and humility. A wrong attitude might be anger, pride, or apathy. If you start off just sure you won't be answered, you'll probably be right.
I've also found that answers from God frequently require action of me. I receive answers to my prayers most readily when I am prepared before I pray to do whatever he will ask of me. Once I have made that commitment and truly intend to keep it, I am guided by Him.
Answers to prayer can come in different ways. Most often, for me, they are answered through the power of the Holy Spirit. The Holy Spirit makes a direct connection to your heart and mind. You will feel and know your answer when the Spirit communicates with you.
How do you know if you are feeling the Holy Spirit's influence? The Bible gives a good list of evidences of this influence:
Galatians 5:22-23 ...the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, meekness, temperance...
God's touch results in godly feelings and changes in your heart. If you are clinging tightly to dark, angry or doubtful feelings, this can intefere with the Holy Spirit's touch. He will usually not come where He is not welcome.
Also, many prayers are answered through the actions of others. The old story of the man praying to be rescued from a flood illustrates this quite well. He didn't recognize answers to his prayers in the help offered by other people. Frequently, our prayers will be answered in the same way. We must be humble enough to accept and recognize such offers from others. This is one way our Father is able to bless two lives at once; the giver and the receiver of the help.
Finally, becoming proficient at communication with Heaven requires practice. Praying every day will help you to develop a familiarity with your own thoughts and feelings as well as those that are impressed on you by the Holy Spirit. It takes some time and effort, faith and commitment to get close to Father in Heaven, but it is very, very worth it.
Thanks for the detailed answer and work. I really appreciate it.