This is what Easton's Bible Dictionary says about "Prayer."
PRAYER is converse with God; the intercourse of the soul with God, not in contemplation or meditation, but in direct address to him. Prayer may be oral or mental, occasional or constant, ejaculatory or formal. It is a beseeching the Lord (Exodus 32:11); pouring out the soul before the Lord (1 Samuel 1:15); praying and crying to heaven (2 Chron. 32:20); seeking unto God and making supplication (Job 8:5); drawing near to God (Psalm 73:28); bowing the knees (Ephes. 3:14).
Prayer presupposes a belief in the personality of God, his ability and willingness to hold intercourse with us, his personal control of all things and of all his creatures and all their actions.
Acceptable prayer must be sincere (Hebrews 10:22), offered with reverence and godly fear, with a humble sense of our own insignificance as creatures and of our own unworthiness as sinners, with earnest importunity, and with unhesitating submission to the divine will. Prayer must also be offered in the faith that God is, and is the hearer and answerer of prayer, and that he will fulfil his word, Ask, and ye shall receive (Matthew 7:7-8; Matthew 21:22; Mark 11:24; John 14:13-14), and in the name of Christ (John 16:23-24; John 15:16; Ephes. 2:18; Ephes. 5:20; Col. 3:17; 1 Peter 2:5).
Prayer is of different kinds, secret (Matthew 6:6); social, as family prayers, and in social worship; and public, in the service of the sanctuary.
Intercessory prayer is enjoined (Numbers 6:23; Job 42:8; Isaiah 62:6; Psalm 122:6; 1 Tim. 2:1; James 5:14), and there are many instances on record of answers having been given to such prayers, e.g., of Abraham (Genesis 17:18, 20; Genesis 18:23-32; Genesis 20:7, 17-18), of Moses for Pharaoh (Exodus 8:12-13, 30-31; Exodus 9:33), for the Israelites (Exodus 17:11, 13; Exodus 32:11-14, 31-34; Numbers 21:7-8; Deut. 9:18-19, 25), for Miriam (Numbers 12:13), for Aaron (Deut. 9:20), of Samuel (1 Samuel 7:5-12), of Solomon (1 Kings 8; 2 Chron. 6), Elijah (1 Kings 17:20-23), Elisha (2 Kings 4:33-36), Isaiah (2 Kings 19), Jeremiah (Jeremiah 42:2-10), Peter (Acts 9:40), the church (Acts 12:5-12), Paul (Acts 28:

.
No rules are anywhere in Scripture laid down for the manner of prayer or the attitude to be assumed by the suppliant. There is mention made of kneeling in prayer (1 Kings 8:54; 2 Chron. 6:13; Psalm 95:6; Isaiah 45:23; Luke 22:41; Acts 7:60; Acts 9:40; Ephes. 3:14, etc.); of bowing and falling prostrate (Genesis 24:26, 52; Exodus 4:31; Exodus 12:27; Matthew 26:39; Mark 14:35, etc.); of spreading out the hands (1 Kings 8:22, 38, 54; Psalm 28:2; Psalm 63:4; Psalm 88:9; 1 Tim. 2:8, etc.); and of standing (1 Samuel 1:26; 1 Kings 8:14, 55; 2 Chron. 20:9; Mark 11:25; Luke 18:11, 13).
If we except the Lord's Prayer (Matthew 6:9-13), which is, however, rather a model or pattern of prayer than a set prayer to be offered up, we have no special form of prayer for general use given us in Scripture.