Baptists and many evangelicals reject the notion of a sacremental "priest" that is somehow in essence different than mere laity, but still ordain their ministers. A "priest" confers the idea that the person is specially endowed with the ability to stand between man and God. Those who subscribe to the idea of the "priesthood of all believers" do not believe that any intermediary is necessary. That said, they still typically note that God gave "some to pastors and teachers" and so that gets recognized.
Ordination (such as my own), typically comes about after:
- a candidate has expressed a desire to be set apart for ministry,
- has some amount of training (although not always a degree), and
- a vetting process wherein a board (usually from outside the local body) examines the candidate
The ceremony itself typically involves:
- a sermon (come on, we're talking preachers here!) about what ordination means
- a laying on of hands
- a prayer
- a proclamation that the ordinand has been set apart for God's work.
I've seen the laying on of hands restricted to one elder, be open to all ordained visitors in attendance, or even to all in the congregation. Like most baptist & nondenominational things, there is no set liturgy - but it feels better if you have the elements above involved.
My ordination (like most Baptist ordinations) says that it was conferred by Long Branch Baptist Church. Technically, no other church, be they Baptist or otherwise, is under any compulsion to honor it, but in practice, I have never had an issue. One will note, if one reads their diploma, typically it just states that the professors here have found the student worthy of a degree. Technically my ordination is my church recognizing that I have been set apart by God in the same way. There is, to the best of my knowledge, no human authority that can remove it, other than my church.
When I went to the courthouse to be given the right to marry couples, the certificate was considered valid. Later, when an Episcopalian lay member of a prison ministry group questioned my clergy credentials (I was retired, and he was being a bit of a jerk), another Episcopalian priest vouched for my credentials, saying I was duly ordained. In interfaith settings, most sacramental priests understand the difference between a Baptist minister who has actually used his ordination and the guy off the street that just bought an ordination certificate online. In practice, I tend to tell people I am ordained and have a Masters of Divinity, since not all Baptist ministers do. It is a cue to those who understand the value of the M.Div, although in the IT world, a lot people still think I just got a certificate. When I tell them it took 8 years, and that I pastored a church for 4, then I get the "ooh"'s of recognition.