Catholic
The Catholic Church teaches that Holy Orders is a sacrament conferring an indelible character, in three degrees — deacon, priest, and bishop — by which men are set apart to teach, sanctify, and govern in Christ's name. It holds that only bishops can ordain, and that the Church has no authority to ordain women.
Source: CCC 1536–1600 ↗
Orthodox
The Orthodox Church teaches that ordination is a holy mystery in which, through the laying on of hands by a bishop, the Holy Spirit consecrates a man to the diaconate, priesthood, or episcopate. It holds that ordination is reserved to men, continuing the apostolic ministry within the life of the Church.
Source: The Orthodox Faith, Vol. II — Holy Orders ↗
Lutheran
Lutherans teach that no one should publicly preach or administer the sacraments without a regular call to the office of ministry. They hold that ordination is the Church's public rite of calling and sending ministers of Word and sacrament, while the ministry itself derives its authority from Christ's institution.
Source: Augsburg Confession, Art. XIV ↗
Reformed
The Reformed tradition teaches that Christ has appointed ordinary, perpetual offices in his Church — ministers of the Word (elders) and deacons — to which men are set apart by election and the laying on of hands. It holds that ordination is the Church's solemn recognition of Christ's call, not a sacrament conferring grace.
Source: Form of Presbyterial Church Government — Of the Officers of the Church; Of Ordination of Ministers ↗
Baptist
Baptists teach that the local congregation, under Christ's lordship, calls and sets apart its own pastors/elders and deacons — the two scriptural offices. They hold that ordination is the church's recognition of God's call and gifting, exercised through democratic congregational processes, not a sacramental rite.
Source: BFM 2000, VI (ordination as such is an inference from it) ↗
Methodist
Methodists teach that ordination sets apart deacons and elders for lives of service, word, sacrament, and order, conferred by bishops through the laying on of hands. They hold that both women and men are called to ordained ministry, and that ordained persons serve within the connectional life of the Church.
Source: UMC What We Believe ↗