Just 50 years ago, if someone moved away without leaving a new address, it could be impossible to find them again. Fortunately, with the advent of the Internet, people are much easier to relocate than they once were. If a friend or neighbor of yours moved away and all you have is their name and former address, it is entirely possible to track them down and even to find their new address.
Call the postmaster for the area where the person last resided. This is the person who is in charge of the post offices for a specific region, and these workers tend to have access to more information than regular post office employees. If the person left a mail forwarding address, the postmaster might able to give it to you. See the resources section for the USPS postmaster finder information.
If the person has asked that their forwarding address be kept private, the postmaster will not be able to give you their new address and you will need to try a white pages website. Peoplefinders.com is a national white pages website that searches public records. You can enter the last address that you have and see if a more recent address is listed.
Try a search engine. It is entirely possible that a search of the person's name or last known address could turn up a current email address or perhaps his workplace information. You could then use this information to call or email and ask the person for their new address.
Check your social networking sites. If you are friends with the person on a social networking website, check out their profile page. Oftentimes, people have their addresses publicly listed. Or, if you do not want the person to know you are looking for their address, you could try asking one of their friends on the site for their most current address.