What do I do when I do not know where the other person is?

When a person cannot be located or is avoiding service, service by publication may be used. To serve a person by publication the summons along with a statement of how to get a copy of the pleading must be published in a newspaper for four successive weeks. Counties may have specific rules about which newspapers meet the requirements for service, to find out more information ask your local law librarian.
The Service Members Civil Relief Act is a federal statute that explains the requirements for serving an individual who is in the military.
Resources:
•    Rule 4.1 of Arizona Rules of Civil Procedure
•    Rule 4.2 of Arizona Rules of Civil Procedure
•    Service Members Civil Relief Act website
•    Maricopa County service by publication form