How does one get fever of unknown etiology?

Depends on the cause: A fever of unknown origin by the modified petersdorf criteria is defined as a fever of 102 lasting at least 3 weeks with at least one week of medical evaluation and still no diagnosis. Acquisition depends on the cause.

Unknown: As dr. Dretler has suggested, this is a medical definition of a condition which may be due to numerous causes. Usually the best way to resolve this is to be evaluated by an infectious diseases expert.