Yes. I'll outline the specifics for one denomination, the Presbyterian Church in America, that baptizes both adults and infants, so you can get a picture of how both situations are handled.
There are a few requirements that apply to both infant and adult baptisms:
- A baptism must administered by an ordained minister.
- It must be done under the supervision of the elders of the church.
- It must be done in the presence of the congregation.
- The minister baptizes by sprinkling or pouring water on the head while saying the words, "I baptize you in the name of the Father, and of the Son, and of the Holy Spirit."
In the case of an infant baptism, the child must be presented by one or both parents, or "some other responsible person." The minister then provides some words of instruction regarding the nature and purpose of baptism, and an exhortation to the parents to raise the child in the fear and admonition of the Lord. After reading the covenant promises, from Acts 2:39, Genesis 17:7, and Acts 16:31, he asks three questions to the parent(s), who answer in the affirmative:
- Do you acknowledge your child’s need of the cleansing blood of Jesus Christ, and the renewing grace of the Holy Spirit?
- Do you claim God’s covenant promises in (his) behalf, and do you look in faith to the Lord Jesus Christ for (his) salvation,
as you do for your own?
- Do you now unreservedly dedicate your child to God, and promise, in humble reliance upon divine grace, that you will endeavor to set before (him) a godly example, that you will pray with and for (him), that you will teach (him) the doctrines of our holy religion, and that you will strive, by all the means of God’s appointment, to bring (him) up in the nurture and admonition of the Lord?
The minister has the option of asking the congregation:
- Do you as a congregation undertake the responsibility of assisting the parents in the Christian nurture of this child?
Finally, the minister is to pray, baptize the child, and conclude with prayer.
These children are then considered "non-communing members," meaning that, though they are members of the church, they may not take communion until they are older and make a profession of faith similar to the one made by adults who are baptized (see the next section).
In the case of adult baptism, the elders of the church are responsible for examining the prospective member in terms of both "knowledge and piety." Afterwards, the person makes a profession of faith in the presence of the congregation, and the minister may admonish the person regarding the seriousness of the obligations that he or she has taken on. The profession typically includes affirmation of the following questions:
- Do you acknowledge yourselves to be sinners in the sight of God, justly deserving His displeasure, and without hope save in His sovereign mercy?
- Do you believe in the Lord Jesus Christ as the Son of God, and Savior of sinners, and do you receive and rest upon Him alone for salvation as He is offered in the Gospel?
- Do you now resolve and promise, in humble reliance upon the grace of the Holy Spirit, that you will endeavor to live as becomes the followers of Christ?
- Do you promise to support the Church in its worship and work to the best of your ability?
- Do you submit yourselves to the government and discipline of the Church, and promise to study its purity and peace?
The person is then baptized, and the minister closes with prayer. The baptized individual is now a communing member of the church, and thus may take communion.