What is the mental representation of God during prayer? In the Bible, we find an internal representation of God, who is within us. For example:


  “Neither shall they say, Lo here! or, lo there! for, behold, the
  kingdom of God is within you.” (Luke 17:21)


but there is also an external representation of God. For example:  


  39 Acknowledge and take to heart this day that the Lord is God in
  heaven above and on the earth below. There is no other. Deuteronomy
  4:39


It appears in today's (western) culture, people pray and "look up to the sky" or have a mental representation of talking with a human form of God (praying to the human Jesus).

In addition, we also believe that God is Omnipresent.

Question:
During prayer, what should the mental representation of God be? 

Should it be a representation of God as the spirit within (so we are focusing inside of our-self during prayer - closing out all the external), to the more external ambiguous God "in the sky", to a human form (to Jesus) or to something that is more like a "force field" (omnipresent)?
"Should" is going to be contingent upon your faith. I don't pray to an all powerful mystical being that is ready to cast me in to the pit of brimstone and fire... I pray to a loving Heavenly Father, on my knees and with a bowed head, and in the name of Jesus Christ.

To me, prayer is an act of the the will of the Father and the will of the child converging. I do not pray to bend the will of God, but to understand His will for me.

However you actually do pray and what ever the differences in Faiths are, I think it is important to pray often and develop a relationship with your Heavenly Father.

The Bible teaches how to pray, but I think the O.T. teachings and with animal sacrifices has been replaced by the N.T. teachings after Christ's life.

John 13:14 teachings to Pray in Christ's name, "And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son."

John 16:23-24 also teaches to pray to the Father and in Christ's name, "23 And in that day ye shall ask me nothing. Verily, verily, I say unto you, Whatsoever ye shall bask the Father in my name, he will give it you. 24 Hither to have ye asked nothing in my name: ask, and ye shall receive, that your joy may be full"

Luke 18:1 states that we should pray often and that we will be strengthened by it, " 1 And he spake a parable unto them to this end, that men ought always to pray, and not to faint;"

Philip 4:6 teaches that we should give thanks, "Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God."

Fist Thessalonians 5:17 teaches to pray very often, "Pray without ceasing."

Mathew 6:5-6 teaches to pray in private and condemn the Pharisees the pray in public for the merit of man, "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. 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."

Mathew 6:7 teaches that we should pray from our heart at that moment, not a pre-rehearsed or memorized prayer, "But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking."