What is the LDS statement on mediums or channeling?
Mediums and channeling both fall under the umbrella of occult practices. All such practices are covered by the following Church policy (General Handbook: Serving in The Church of Jesus Christ of Latter-day Saints, Section 38.6.12):
“That which is of God is light” (Doctrine and Covenants 50:24). The occult focuses on darkness and leads to deception. It destroys faith in Christ.
The occult includes Satan worship. It also includes mystical activities that are not in harmony with the gospel of Jesus Christ. Such activities include (but are not limited to) fortune-telling, curses, and healing practices that are imitations of the priesthood power of God (see Moroni 7:11–17).
Church members should not engage in any form of Satan worship or participate in any way with the occult. They should not focus on such darkness in conversations or in Church meetings.
Isaiah 8 clearly teaches against such practices as trying to speak with the spirits of the dead:
19 And when they shall say unto you, Seek unto them that have familiar spirits, and unto wizards that peep, and that mutter: should not a people seek unto their God? for the living to the dead?
The Old Testament includes many instances where the Lord commanded his people not to tolerate such things, and other volumes of scripture include stories or counsel regarding such things (see the Topical Guide entry for Sorcery). Of particular interest to you may be the story starting in Acts 16:16 where Paul casts an evil spirit out of a woman who “brought her masters much gain by soothsaying”; and the chapter “Religious Enthusiasm among Early Ohio Converts” in Revelations in Context along with the corresponding sections of the Doctrine and Covenants, which covers some early confusion among the saints regarding the influence of spirits.
Hopefully these clarify not just the policy of the Church in the latter days, but also the Lord’s commands about such things from the beginning. Such things ought to be avoided by those who follow the Lord Jesus Christ.