Ask your parents to help you choose a question from https://goo.gl/ECSdXj and ask one of your parents or grandparents to answer the question for you. (You can even call or facetime someone if you aren’t near enough to ask them in person.) You may find that you want to have several questions ready so you can hear more stories. :)
Start a journal. You can record it digitally or on paper. If you haven’t learned to write yet, ask someone to write while you tell them what to write. Or draw a picture and then have someone write down what the picture is about. Be sure to keep whatever you do in a safe place so you can someday share it with your own kids.
Do the monthly family history task in the Friend magazine. It’s called Family History Quest and you can do it in the hard copy of your magazine or online here.
If you have learned to type, you can try indexing. Go to https://goo.gl/Dsh17G to learn how. Learning will take about 15 minutes. Then come back another day and choose a beginning indexing project. They usually take about 15 minutes. You will probably want to stick with beginning projects until you get good at reading cursive.
Adults and Teens:
Download the “Take a Name” app to a phone or tablet and link it to your family tree. (It will find names in your family tree that are ready to have their temple work done. All you need to do is print the cards and take them to the temple. The app may take 24 hours to find names, but it can do it in the background while you do other things. If you can, please give a one-time donation so the app makers can keep the app updated and bug free. This is not a Church affiliated app, though it is made by members of the Church.)
Go to https://goo.gl/ECSdXj and choose one of the questions, then record your answer to this question in a journal, in a computer doc, or in an audio version. If you want to preserve the answer for posterity, go to familysearch.org and click on memories and you can upload it (you can scan handwritten items or photos, or you can upload typed or audio files).
Go to https://goo.gl/ECSdXj and choose a question to ask an older relative. (Or go visit someone in the Legacy branch and ask them; you’ll make their day!) Be sure to record the information for posterity in either written, typed, or audio form. Then upload it to familysearch.org and link it to the person who told you the story. For an explanation on how to do that do a search for “upload memories to FamilySearch” on youtube and watch the video that most closely matches what you are trying to do (or ask your ward consultant for help).
Try indexing. Go to https://goo.gl/Dsh17G to learn how. Learning will take about 15 minutes. Then you can come back another day and choose a beginning indexing project. If you end up not having time to finish it right then, you can save it and come back later to finish. (Projects not finished after a week will be turned over to someone else to finish.)
Gather all your own family history documents (birth certificates, marriage certificates, etc.) and put them in one place.
Use the “My Family” booklet to record family stories and memories for yourself, your parents, and your grandparents. It’s available online; get the instructions for using it here; or you can buy a hard copy of it at the LDS Distribution Center (or online) for 50 cents. If you do the hard copy, then ask someone to help you transfer the information to familysearch.org when you’re done so the stories can be preserved and shared with posterity.
Use the “Find Your Family Names” pamphlet to get started on family research. It has three different tracks to use depending on whether you have no family history done, some done, or a lot done already, so it can be useful no matter what level of family history has already been completed in your family and no matter how much you know about doing family history. You can access that pamphlet online here or purchase a hard copy at the LDS Distribution Center (or online) for 50 cents.
Scan and upload family photos to familysearch.org (especially historical photos) and tag the people in the pictures. You can also doing this using the “Family Tree” (i.e. FamilySearch) app on your phone (you can even scan using your phone, so this can be a good option if you don’t have a scanner).
Go and look at your family tree on familysearch.org. (To sign up, all you need is the membership number on your temple recommend [or from your ward clerk], if you want to be able to do temple ordinances for ancestors. Signing up will only take you a few minutes and they will talk you through the process online. Or you can ask your ward consultant for help.) If you look at your family tree in portrait mode, you will see ancestors with record hints and you can start by looking at these and seeing what is helpful to you.
Go to https://www.familysearch.org/partneraccess and sign up for a free account with one (or more) of these other genealogy websites. I recommend starting with https://www.ancestry.com/. Signing up will only take a few minutes, then be sure to let them link to your family tree on familysearch.org. Come back in a day or two and see what “hints” have appeared (look for the leaf with a number by it at the top near your name, after you sign in). You can filter for a specific family or just browse starting at the top. They’ll walk you through what to do and you can spend as much time as you’d like each time you visit (they pretty much never run out of hints).
Download the “Family Tree” app (it’s the familysearch.org app) or just go to https://www.familysearch.org/photos/people and choose a person in your family. Once the person’s info is pulled up, click on the memories tab and look at the content that has already been uploaded. See what new things you can learn about that family member. If you have memories of your own you’d like to share (photos, audio, written accounts, etc), you can upload them using the app or your computer.
Play around a little with the “Family Tree” app or the familysearch.org website
Search for historical records.
Look for ancestors with tasks (the tasks are usually relatively simple and they walk you through it).
Look for ancestors ready for temple work. (Look for ancestors with a temple icon near them. Then click on it and see what is needed in order for you to take them to the temple. Some of them just need you to reserve their names and print their cards.)
Find out how you’re related to people around you who are also using the app (you both have to have the app open and agree to look for the relationship at the same time).
Record your own memories, etc.
Reconnect with relatives you haven’t seen for a while by phone, email, Facebook, etc.
Start a journal. Try to establish a regular time to write. Maybe on Sunday evenings or as a family during Family Home Evening
Tell your kids stories from your childhood and stories you’ve heard from your parents, grandparents, etc.
If a lot of your family history work has already been done and you don’t know what else to do, try going to puzzilla.org. It is a branch of FamilySearch and they will walk you through various options that can help you figure out where there is still work to be done.
Contact your ward consultant and ask them to help you figure out where to start. They’ll be happy to be able to magnify their calling!
Family history libraries are also a wonderful resource. They are staffed with knowledgeable people who are ready to help.