This is a great question that brings two answers/camps that typically leads to source of contention among Reformed Christians and Churches. Depending on what you believe will typically also influence what type of church you are a member of.
Reformed Christians believe in one of the following two in regards to Baptism:
- Credobaptism - or the literal translation, Believers Baptism (credo is latin for "believe".) maintains the belief that only those who make a profession of faith should be baptized. As such, they do not baptize infants because not only can infants not make a profession of faith, but also because there are no directly recorded instances of infants being baptized in scripture.
- Paedobaptism - or the literal translation, Child Baptism (paedo is derived from greek for infant/child) maintains the belief that you baptize both professing believers and their young children. Thus the term paedobaptist is somewhat misleading as they don't just baptize young children or infants. Although there is no direct mention in scripture about baptizing young children, they hold to the belief that the logic of baptism flows from a covenant-keeping God, who blesses His people in a similar fashion He did in the Old Covenant.
Both camps use a variety of scripture to support their position, and both bring valid arguments. As to which belief is correct, we leave that to you to discern. However here's some resources from both sides to guide you in this.
Resources for further study