Take advantage of immigration records
Once you've begun to piece together a picture of your Jewish ancestors, you can look into immigration records. These are especially useful if you know which family members immigrated and where they came from, as they can tell you more about what happened.
Unfortunately, immigration records can be confusing and difficult to navigate. Most immigrations between 1820 and 1982 are documented in the National Archives, though there are undoubtedly gaps due to poor record-keeping.
There is also a significant amount of paperwork that must be completed before you can access an immigration record that is less than 75 years old. This includes a request under the Freedom of Information Act (FOIA). (More information can be found here.) Records older than this can be freely accessed, and many of them are available online for free.