Visit their last known address and ask neighbours for any information that might help. If they cannot help they can often direct you to someone who can. Visit your local library and check through the countrywide telephone directories. Larger libraries may have collections of telephone directories from around the world and you should also be able to access many of these via the Internet. Place an advertisement in the local newspaper Write to the appropriate local newspaper.
Editors are usually happy to print features or advertisements about missing persons.
If you want to spread your search nationwide try one of the national newspapers. Check electoral registers If you have an address try searching the relevant electoral registers. These will be found in the local reference library or county record office and can help you to establish how long a person lived at that address. The disappearance of a family member from the registers often means that they have moved home, married or died. Even if you do not find a death entry it is worth checking the will indexes as the missing person may have died abroad on holiday or business or while on duty with the armed services.