One of the Articles of Faith of The Church of Jesus Christ of Latter-day Saints addresses this question:
We believe that a *man must be called of God, by prophecy, and by the laying on of hands by those who are in authority, to preach the Gospel and administer in the ordinances thereof. (Articles of Faith 1:5)
*As evidence that "man" here refers to humanity generally and not just males specifically, consider that the church's missionary force--set apart by the laying on of hands to preach the Gospel--includes thousands of women.
Callings in the Church
It is not at all unheard of in my faith for people to be given advanced noticednotice by the Holy Ghost about an upcoming calling to serve in a particular capacity in the church, but God's house is a house of order. To serve with God's authority, it is necessary to be called to that position by the person holding the requisite priesthood keys. It is not inappropriate for someone to inform their Bishop (or other priesthood leader) that they feel impressed that they are to prepare to serve in a particular calling, but the calling must still come through the leader holding the keys.
We also publicly sustain people when they are called to a given capacity--the Doctrine & Covenants explains the importance of it being publicly known who has been called to what position:
Again I say unto you, that it shall not be given to any one to go forth to preach my gospel, or to build up my church, except he be ordained by some one who has authority, and it is known to the church that he has authority and has been regularly ordained by the heads of the church. (D&C 42:11)
This helps us support one another in our callings, and serves as a preventative measure for usurpers who may wish to lead people astray.
For more information, see Callings in the Church
Gender
The process described above is the same for men and women. We also believe that God has given different roles & responsibilities to men & women. See, for example, The Family: A Proclamation to the World. Some callings are given to both men & women; some callings are given only to men; some callings are given only to women. Both men & women preach & pray in public services.
Both men & women have access to priesthood power in their callings; only men are ordained to priesthood offices (e.g. deacon, bishop, apostle, etc.)