What is the difference between Christening, Infant Baptism, and Infant Dedication?
First of all, you need to understand that not all churches define these terms in the same way. That is what makes it difficult to understand.
For those churches that believe in Infant Baptism (Methodist, Presbyterian, Episcopal, Roman Catholic, Orthodox, Luthern, etc.), Holy Baptism is a sacrament (a sign/action) where God does something. Baptism is the New Covenant form of initiation into God's mighty actions just as circumcision was the Old Covenant's sign of initiation for a child (see Colossians 2:11-12). In other words, Baptism is a sign that God claims the person as a child of God and is incorporating them into the community of faith. Just like circumcision, the child will have to decide one day for him or herself whether they are going to let the sign (and God's love) mean anything to them or not. When the child is 12 years old, it is hoped they will attend a Confirmation class so they can have their questions answered about God and faith...and be given the chance to decide what they believe. It is at that point, if they do desire Christ as Lord of their life, that they are encouraged to make a public confession of their faith. This is the much more ancient view of Baptism and is held by well over 90% of the Christians in the world.
However, there are some churches that have a different definition for Baptism (Church of Christ, Church of God, Southern Baptist, etc.). They define Baptism as a sign/action where the person is doing something. They believe the sacrament is a way for us to publically confess our faith...and therefore, only someone who understands a little about Jesus, forgiveness, and salvation can participate. This is called adult or believer's Baptism. It is in these churches where Infant Dedication is practiced. That ritual (and this is where it gets fascinating!) uses remarkably the same actions as an Infant Baptism. They hold up the baby and say "thank you God for giving us this child. This child really belongs to you. Help these parents, and our church family, to raise this child of God up so that one day he/she may choose to follow you." Believer's Baptism was begun by the Anabaptist movement in the 1500s.
So, the two practices (Infant Dedication, Infant Baptism) are remarkably similar in actions performed. The big difference is found in how we define what a sacrament is....grace-driven (an infant doesn't do anything to earn God's love in Baptism) or action-driven (believer's have to repent, confess, and believe to be able to receive the sacrament). It would take longer to discuss how the difference in these two approaches helps define the culture and style of each kind of church. A lot longer.
Now, Christening. Unfortunately the word "Christening" is used by some to mean Dedication and others to mean Baptism. That is why I don't use the term often. It is confusing. In actuality, to "christen" means "to give a name" and then smash a bottle of champagne against it. All in all, I find most parents don't appreciate that custom in regards to their babies.