Although prayer has many forms and many purposes, at it's most basic, it is simply a conversation between you and God. It can be formal or it can be casual. You can recite a prayer such as the Lord's Prayer or you can talk to God in a very free and natural way. You can pray alone or as a group. You can pray out loud, silently in your head, or even with paper and pen. You can pray by singing a worship song, or reading a Psalm. God will always hear you no matter what form your prayer takes.
Just as you may talk to your friends and family about a variety of topics, you can talk to God about anything. It's most common to praise God, ask for forgiveness, thank him, or ask for things that you need, but you can also tell God what you're feeling or just about anything else that's on your mind. For example, you can ask God to help you pass an exam, thank him for your friends, confess that you were insensitive to your wife or comment on how difficult your job is getting. Any topic that is important to you or important to God is appropriate.
Some people prefer to be formal and only pray when they are kneeling with their eyes closed. Others will pray in the shower, in the car or wherever they happen to be. There is no right or wrong way to pray so long as it's sincere. When you're praying, God deserves to have your complete attention, so if you need to find a quiet place in order to do that, then you should do so. On the other hand, if you can focus on God while sitting in the middle of a crowded cafeteria at lunch time, then that's perfectly acceptable too.
If you're ever in the position that you want to pray but don't know what to say, you can always recite the Lord's prayer found in Matthew 6:9-13. Another method is to find one of the Psalms which reflects what you're feeling or what you want to say to God. You can recite it our loud to the Lord, or read in quietly while contemplating God's presence.
What matters most is how often you pray. God wants to spend time with you! In order to have a close and intimate relationship with God, you will need to make prayer a priority rather than fitting it in whenever you have time.
When you begin to make prayer a priority, an interesting thing happens. You become filled with God's love and closeness and you will want to pray more and more. The more your pray, the more you will want to pray until eventually, you are spending time with God in everything that your do.
In 1 Thessalonians 5:17, Paul tells us to "Pray without ceasing." Paul does not mean that we should be on our knees in earnest prayer at every moment of our lives. Obviously, we need to work, to eat and to sleep. What Paul means is that we need to constantly have an awareness of God's presence and share with Him everything we do. For example, even when we are at work, we can be aware of God's presence, feel the peace and guiding of the Holy Spirit and consider how God wants us to respond to the world around us. Though we may not be engaged in conversation constantly, we can always feel God with us everywhere we go, just as we would a friend who is always beside us.