PRAYER
All bible quotes are from the King James Version unless otherwise noted.

CHRIST'S INSTRUCTION

Jesus Christ gave a basic outline of how to pray (Matthew 6:9-13):

Our Father which art in heaven, Hallowed by thy name
(we must direct our prayers to the Father, and acknowledge the holiness of his name)
Thy kingdom come, thy will be done on earth, as it is in heaven
(pray for things that are in harmony with God's will for earth and heaven)
Give us this day our daily bread,
(it is okay to pray for our sustenance for each day)
And forgive us our debts, as we forgive our debtors
(our debts to God are our sins - Romans 6:23 - , it is good to ask for forgiveness, and forgive others)
And lead us not into temptation, but deliver us from evil.
(and we should pray for strength to overcome temptations and sin).

SCRIPTURAL PARAMETERS

Jesus Christ instructed that we pray to the Father (Matthew 6:6), in his (Christ's) name, as Jesus himself will grant what we ask of the Father (John 14:6, 13-14). This is because he is the mediator between God and men (1 Timothy 2:5).

We are not to pray for harm towards others or for selfish gain. All prayers must have a good motive behind them. (James 4:3).
So don't be surprised if the prayer for your co-worker's demotion doesn't happen, or if your prayer for winning the lottery doesn't happen, or if your prayer that your wife gets chicken-pox doesn't happen, etc.

We are not limited as to how often we should pray. (1 Thessalonians 5:17, Matthew 26:41, Acts 10:2, Ephesians 6:18)
Don't be restricted to only recommended times of the day. Pray whenever you want, or need, to.

We are not to pray in a showy, boastful way; prayers must be modest and humble. (Matthew 6:5, Luke 18:9-14).
Go ahead and raise your hands, or bow your head, or kneel, or whatever. Just don't fret if people aren't noticing you doing it; and don't make it a point to be noticed.

It is proper to pray for others' well-being (James 5:13-16).

Do not pray excessively repetitive prayers (Matthew 6:7).
This would include rosary repititions.

You must believe in the power of your prayers in order for them to be heard (Matthew 21:22, Mark 11:24).

Don't waver in your request. Be sure of what you are asking (James 1:6-8).
If you aren't sure of your request, wait until you are sure before you pray for it.

CONCLUSION

In a nutshell, prayer should be directed to the Father thorugh the name of Jesus Christ as our mediator. Prayer should be spoken with a motive towards the love and wellbeing of others, one's actual needs (instead of greedy desires), and with humility. Pray for those who are sick, or poor, or injured. Pray for those who need comforting, or spiritual strength. Pray for help when you are in need, when you are scared, when you are at a crossroads in life. Pray for your faith to be strengthened, pray for direction when tackling tough decisions. Pray for protection and help when danger threatens. Pray for wisdom and knowledge. Pray to resist temptations . Pray for forgiveness when you sin . Pray for your enemies. Pray for children . Pray for help in your Christian labor. Pray for one another:
Genesis 20:7, Nehemiah 1:6, Matthew 19:13, Matthew 26:41, Luke 6:28, Luke 10:2, 1 Thessalonians 5:25, James 5:14,16, etc.