As you move back in time finding one ancestor after another, eventually you will reach a point where you can't seem to move back any farther. We call it "a brick wall." Like any wall, while you can't go through it, you can find away around it. This means that you will need to approach the problem differently than you usually do.
Look at other people in the family, besides your direct ancestor. Sometimes we approach genealogy like a horse with blinders on. We often want to look just at our ancestor when looking his/her siblings and their spouses would help us more. I recently documented a family more completely by looking at the second wife of an ancestor. The wills of her parents gave me the information I needed.
Start from last known fact. Forget what your cousin told you. A fact is something you can prove with documentation, not something you suspect is true.
List all the people in the generation of the "Missing Person."
Next look for records of people who married into the family.
Look at the neighbors. In years past neighbors were often also relatives. You can find them by using census records and land records.
Use a variety or records. Look for wills, deeds, city directories, tax records, social security records, school records, voting registers etc.
I had a research problem sorting out two women by the name of Sarah, who had fathers who were brothers. I couldn't prove which Sarah I needed until I traced and proved the other Sarah also.
Put your ancestors into the context of the time they lived in by learning about the history of the time and place they lived in. What was happening in the community and in the world during the lifetime of your ancestor? Check out newspapers of the day to find out how your ancestors lived. You can put together a history of a person with not too many facts, by pulling in the history of the period. Develop a timeline or chronology by making a chart beginning the year your ancestor was born. In three parallel columns list the year, the age of your ancestor and the event, ie.1818 age 18 she married. Use this to track events for as many ages in their life as you can. How old was your ancestor during wars, famines, the opening of new lands? Knowing what major events happened in the area he lived in will give you clues about where to check for records.
Organize and re-evaluate the information you have. Using your timeline plug in everything you know. Read again any letters, the backs of photos, and stories from interviews you have done. If you haven't done any interviews, this would be a good time. Learn to tell your ancestors life story like a biography from beginning to end, it will help you understand who they really were.
If the "older generation" now includes you, then check with cousins to learn what stories they have heard. Write down what they say even if it doesn't agree with what you believe. The blending of family remembrances solves many problems. Make certain to document "who" told "what story," and include it with the account of the event.
If you are stuck, maybe you need to "sharpen the saw" and learn some new skills.
Learn to use the many resources available to you. The internet especially is loaded with help including databases (www.ancestry.com), free online classes and tutorials (http://ce.byu.edu/is/site/courses/freecourses.cfm), and free online genealogy interest lists (www.rootsweb.com ). You can borrow books at the library or through inter- library loan and microfilm can be borrowed for a small mailing fee through your local LDS Family History Center. You can view their online catalogue at www.familysearch.org.
Take a good long look at a map of the area you are searching. Did your ancestor live near the border to another state or another county? You may need to look at neighboring localities. Did they live along a water way that would have carried them easily to another city? While you can't go through a "brick wall," you can go around it or over it by looking for another route.
You can direct questions to me at firstname.lastname@example.org.