I am a "non-denominational Christian" (well, my church is HQ'd out of Church of God; Anderson, Indiana in case anyone wants to know).
My understanding is that Catholics and similar denominations, such as the Church of England, practice "christening". This practice is done with an infant whereby water is sprinkled onto the head of the baby, bringing him or her into the grace of God. It is essentially baptism for infants as I do not recall Catholic believers ever having this rite with water again (maybe someone else can help me out here). Sometimes it's called "christening", sometimes it's called "baptism".
Other Protestant denominations, such as my church, do not believe that a baby is capable of making this decision for him or herself and therefore christening is not done. Instead, we practice "baby dedication" and "adult baptism".
In baby dedication, the parents present the baby to the church congregation and pledge to do their best to raise the baby in a Christian home. There is no water sprinkling involved; though some churches annoint the baby's forehead with oil. What the parents are saying is that, they will try to raise the baby with Christian ideals, but also recognize that their child will have to decide for himself when he is old enough. The event is low-key and just a short presentation during a regular church service.
My church practices adult baptism by immersion. There comes a point in time when a person decides that Jesus is the way to go and decides to pray to God to ask him for forgiveness and ask for help in leading the right kind of life - in effect, they "become a Christian". One of the next steps for new believers is to make their public statement of faith through baptism. There is no age cut-off; I've seen people as young as 13 to as old as 40+ go through baptism. They key here is for the believer to choose to do it when *he or she is ready*.
For example, being that my [Polish-American] family is Roman Catholic, I was christened in a Catholic church when I was a baby. However, my family never went to Mass (my parents were non-practicing Catholics). By my own accord, I chose to become a Christian when I was 14. Two years later I decided that I wanted to be baptized again, this time by my choice, and went through another baptism at age 16.
My church conducts baptisms during a regular church service a couple times a year. That is, people who want to be baptised usually all go on the same day. This rite usually takes place inside the church as most churches have a "baptismal" or a big jacuzzi or bathtub-like tank right in the sanctuary which is filled with warm water for this occassion. The participant steps into the water-filled baptismal with the officiating pastor. Sometimes a friend or relative goes in too for moral support or to share in the happy occassion. The participant is asked by the pastor to verbally confirm his or her faith in Jesus Christ and his or her desire to be baptised.
In line with the account of Jesus' baptism in the New Testament, the participant is gently tilted backwards by the pastor and "dunked" momentarily. Yes, that means the believer gets soaking wet!
Just in case anyone is sincerely wondering, I'll add that everyone is fully clothed for this.
Of course, individual denominations will have slightly different takes on the subject. At any rate, I hope this helps further some understanding!
.....Kelly