Finding a person's previous address isn't as difficult as you might think. If you're willing to keep checking options and asking questions, including slogging through a lot of old records and paperwork, finding out where a person used to live is actually fairly simple as far as detective work goes. Additionally, there are numerous search engines that can make the job an even easier one.
Collect all the information you can about the person whose previous address it is you're looking for. You should have their full name (including middle name if possible), age, maiden name (if applicable) and any other useful information such as their social security number.
Conduct a search using a reverse lookup engine. These search engines will check a person's name against records for addresses and sometimes phone numbers. Some of these engines cost money, but others such as 123 People are free of charge.
Contact the county courthouse in the area that a person used to live. If you ask to see tax records or marriage records for that person, those records will have their previous address on them. If you want copies of the records you'll be required to pay a copying fee, but often just looking at public records is free of charge.