To Turn the Hearts, page 19 states:
The high priests group leader directs the work of family history consultants as he:The question is, who trains the Family History Consultants? Here are the duties of a Family History Consultant from pages 19 and 20 or the Leader's Guide:
- Recommends members to be called and set apart as family history consultants, as requested by the bishopric.
- Works with the bishopric to ensure that enough consultants are called to meet the needs of the ward.
- Provides assignments to consultants, including assignments to work with certain ward members.
- Ensures that consultants are properly prepared to perform their callings and makes them aware of the training resources at FamilySearch.org/serve.
The bishopric and the high priests group leader determine how many family history consultants are needed in the ward. The high priests group leader directs their efforts.
Consultants are skilled teachers who work and communicate well with others. Wile consultants need not be experts in family history research, they should be comfortable using the resources at FamilySearch.org and helping others use them. These FamilySearch resources include family pedigrees, historical records, and the FamilySearch indexing program. Youth can be called to serve as consultants when their technology skills can be helpful in assisting others.
Consultants register at FamilySearch.org/serve to receive information, training, and updates from the Church.The training is right there on LDS.org and FamilySearch.org. Here is the link to the training materials.
So the answer to the above question is that the training comes from the Church's websites. I would think it to be important that the Ward's High Priest Group Leader also review the training so he can properly support the Family History Consultants.
Here is a quote from Elder D. Todd Christofferson in the Religious Educator, vol. 6, no. 2 (2005), 10–11:
“If I were a bishop again, my approach would be to charge the high priests group leader with the responsibility to lead out in the ward council on this subject. I would ensure that we had one or more . . . family history consul- tants who were ‘people persons’ who could work under his direction. . . .Does this sound like your Ward?
I imagine that in the course of a year we could help at least ten families. In five years, we could have a corps of fifty families active at some level in family history and its attendant temple work. That to me would be a successful, well-run program.”