If your ancestor arrived in America before 1820, finding passenger lists becomes more difficult. Often you must rely on print resources to find these early immigration records.
One of the best resources for these passenger lists is Passenger and Immigration Lists Index by P. William Filby (often just referred to as 'Filby's'). This is an index to published immigration lists found in periodicals or reference books. Supplements to the original three volume index are published annually.
Filby's now contains over five million records. You must search the original three volume set and each supplemental volume which can be time consuming--but is well worth the effort! Filby's may seem intimidating but it is actually easy to use.
To use Filby's, search for your ancestor's name. Each volume is arranged alphabetically by last name and each entry may include a birthdate, the port entry and the date of entry. There will also be a source identification number and page number. Once you find your ancestor, make a note of the source and page number. At the front of the volume, you'll find all of the print resources listed by their source number. You can find some of these resources in the Glenview Public Library. The others you can locate with WorldCat.
For example, I search for Alexander Sessions and find him listed in one of the volumes. The information I find shows that Alexander Sessions arrived in Massachusetts in 1677. The source number is 3274 and the page number is 213.
Next, I search for source number 3274 at the front of the volume. 3274 is the number for the book: Directory of the Ancestral Heads of New England Families. I will find Alexander Sessions on page 213 of this book.