What's in a Name? Understanding Jewish given names

We're all familiar with nicknames and diminutives in our native languages. Many of use are unfamiliar with Hebrew and Yiddish names and their variations. Records of Eastern European Jews most often use a person's Hebrew or Yiddish name, and depending on the time period and place a person lived, may also have a legal secular name. After emigrating from their place of birth or residence, immigrants were free to adopt a new given name. For Jewish immigrants this often meant choosing a name that had no relationship to their original name. How do you find their name? How do you understand the variations of it that might have been used?