Contact the U.S. Credit Bureau to retain a list of previous addresses. A person can often do an Internet search and get results back from sites that have public records published on them, but not all addresses are available this way.
The Credit Bureau does usually have most or all of a person's past addresses because credit card companies and banks contact the Credit Bureau to have the new address put on their credit report. Any address that person has had after incurring any type of credit debt should be in their credit report. Another method is for a person to check the sites with which they have done long-standing retail business, such as Amazon or eBay. They can find any unedited addresses there, as well as a history of purchases with dates to help reconstruct a time line.
If these options do not yield enough results, the person should check old boxes, files, junk drawers or old computer documents for bills, letters or tax documents they may have kept. These types of documents often contain the dates they were written, as well, so putting together the time line of the different residence in which the person lived becomes easier. Friends and family members are often a good resource as they might have old letters or an address book with past addresses.