The general rule is always start with what you know. Talk with older members of the family and write down the names and places they remember. Get all the information you can – names, places, dates, etc. The LDS genealogy website has a number of blank forms that you can print out and use while gathering the data. In addition, go through old family photograph albums; if the photos are labelled with names and/or dates, great. If not, perhaps someone will know who it is. You might be fortunate enough to find someone who can not only identify the person, but who can also regale you with stories about the person in the picture. I find it particularly fruitful to have a cassette recorder running while we go through the album. The stories are great. For additional suggestions, the LDS website has a Research Guidance section.