When you participate in family history, you come to understand your identity and individual worth. Visit with your living relatives to learn as much information about your family history as possible. Then complete a pedigree chart of your family and list the temple ordinances that have been completed for each person.
Knowledge Elective Experience #4 says:
Select a gospel principle you would like to understand better (for example, faith, repentance, charity, eternal families, or baptismal covenants). Read scriptures and the words of latter-day prophets that relate to the principle. Prepare a five-minute talk on the subject and give the talk in a sacrament meeting, in a Young Women meeting, to your family, or to your class. Record in your journal how you can apply this gospel principle in your life.
If you are curious about genealogy (the fancy-schmancy word for family history), you can research that using the resources they have suggested and prepare your talk on what you have learned. These are top-notch resources, by the way! :)
Good Works Elective Experience #6 says:
Spend at least three hours giving service outside your family. Ask your ward or branch Relief Society president or a community leader for suggestions for service. For example, you might take care of children while parents attend the temple; collect, make, or recondition toys or games for a nursery; accept an assignment to clean the meetinghouse; or perform errands for or read to a homebound person or others in need. Record in your journal the reactions of the person you served and possible goals for future service opportunities.
Family history is SERVICE!!!! Finding names, taking them to the temple, and doing their ordinances may be the one of the biggest, most important services you will ever do for other people. I mean, it's their SALVATION we're talking about here, people! Who KNOWS how long people have been waiting to cross from Spirit Prison into Spirit Paradise?! Obviously, you can't do this for all three hours of service, but you can certainly count it.
You can also do family history for a project in most of the values. Be creative!
If you want to get more involved in the work of salvation for the dead (who are NOT actually dead!), familysearch.org is a wonderful resource! Create an account (or log in with your LDS account) and start searching! I promise that you will experience the Spirit of Elijah for yourself and feel your ancestors smiling down on you.
Here are some great recent conference talks on family history. You don't have to read them all in their entirety, but skim over them and if something catches your eye, read it!
Elder Bednar's "The Hearts of the Children Shall Turn" from the October 2011 General Conference is probably my favorite: The Hearts of the Children Shall Turn. If you don't read the whole of this one, please read these: