If the person has never previously been baptized in any church, or if the baptism was not in the proper "form" (if, for example, the person was a convert from 'Oneness Pentacostalism' or LDS), then he will be baptized. If someone was baptized in most any other mainstream non-Catholic Christian church, then that baptism is recognized as valid. If there is any question as to the validity of the person's baptism, they'll do what is called a "conditional baptism".
Sprinkling or submersion?
The Baptism must be Trinitarian. So any regular mainstream Christian sect would be acceptable. Those who deny the Trinity or those with just-too-bizarre conceptions of God (Mormons) are not acceptable.
Baptism is effected by the nature of the process. The pouring or submersion with the intention of Baptising makes it work. One need not have a priest perform it in order to make it valid.
The same is regarded with marriage. Marriage between two Protestants is presumed valid because, again, a priest is not necessary for sacramental validity.
Any Christian may baptise (though this is usually reserved for emergency situations) and any two Christians can sacramentally enter a marriage.
SD