What's the difference between infant baptism and believer's baptism?

In infant baptism, God claims the child with divine grace. Clearly the child can do nothing to save himself or herself, but is totally dependent on God's grace, as we all are — whatever our age. In believer's baptism, the person being baptized is publicly professing her or his own decision to accept Christ. Believer's baptism is an ordinance, not a sacrament. United Methodists baptize people of all ages who have not previously received the sacrament. Even when the people being baptized are believing adults and are ready to profess their faith, our emphasis is upon the gracious action of God rather than upon the individual's decision.

From FAQs About Baptism, Membership, and Salvation

Learn more about baptism -
By Water and The Spirit
This is Your Baptismal Liturgy