What re the responsibilities of Consultants?

Consultants are our "front line" workers. They are listed online as the people to go to for help.

What are the specific responsibilities of our callings in Temple and Family History?
These can be found in the General Handbook: Serving in The Church of Jesus Christ of Latter-day Saints
For example:

25.2.4 Ward (or Branch) Temple and Family History Consultants
Ward temple and family history consultants serve under the direction of the ward temple and family history leader. The bishopric calls these members to serve. Adults and youth may be called. The elders quorum, Relief Society, and Young Women presidents may suggest who could serve.

Consultants teach others in simple ways how to participate in temple and family history work. They have the following responsibilities:

Help members prepare to receive temple ordinances and make temple covenants.

Help members experience the blessings of discovering their ancestors and performing temple ordinances on their behalf. These experiences are especially important for those learning the gospel, new and returning members, and those preparing to receive a recommend for proxy baptisms and confirmations.

Participate in temple and family history coordination meetings (see 25.2.7).

Serve in a local FamilySearch center when assigned (see 25.3.6). [If you had this assignment you would know.]

A personal perspective on helping in family history (Bill Buchanan):
There is a common misconception that Consultants need to be experts at all things concerning family history. But that is the role of FamilySearch Support. Consultants should be able to help with routine things such referring members to the bishop if they need to get a temple recommend, using Ordinances Ready, booking into a temple session, adding people to Family Tree, reserving ordinances and printing temple cards. Any additional skills are a bonus. Much is learned through personal experience. 

To reach free FamilySearch Support, call 1-866-406-1830 (8 am to 8 pm Mon-Sat or 1 pm to 8 pm Sun)  or email North America Support at nasupport@familysearch.org