Talk to family members - parents, grandparents, aunts, uncles and cousins. Since the heaviest immigration occurred between 1890 and 1914, a few of the original immigrants are still living; certainly many of their children are alive. A tape recorder and notebook are your basic tools. Ask the immigrants about their family in the Old Country, their town of origin, reasons for immigration, customs they kept, and the lives they lived. Ask the children and grandchildren of your immigrant ancestors about their childhood -- stories they heard from their parents, foods they ate, holiday celebrations, the interaction of the family with the larger American community, wartime experience.
Keep your questions open-ended, so that they don't elicit only yes or no answers. Don't ask, "Did your father play with you much?" Instead ask, "What's your first memory of your father?" David Weitzman's book "Underfoot" has several excellent chapters on designing interviews, and will be helpful as you plan your questions. The opportunity to ask questions of these people is fleeting, and if you don't carry your research any further at this time, at least do this much. Public records will be available to you later, but the personal recollections of these original immigrants and their children will die with them.
Look for family papers and photographs to reconstruct your family history. For example, Declarations of Intent to Become Citizens will contain valuable information, including the name of the ship and approximate date it docked. Once you know this, ask the National Archives to search Passenger Lists; if they find it, they will send you a copy of the page upon which your relative is listed. Passenger Lists not only have information about family members traveling together, but often names relatives who stayed behind. The fee for this service is nominal.
Many ships records and passenger lists may also be found on the World Wide Web. The 1900, 1910 and 1920 U.S. Census can be helpful in locating those who arrived before 1920. The public library in the capitol of the state where your relatives lived should have the Census for that state on microfilm. In addition, the Bureau of the Census will search census records upon application by you and payment of a small fee.
Contact the Church your relatives attended. For many immigrants, it was the center of their cultural and social lives, and may have birth, marriage or death records of your family. The Church will certainly know the history of that particular congregation, possibly even have it in writing. You will want this information because it will help in your personal research. If you contact the church by mail, enclose a self-addressed stamped envelope. There may be a charge for any record they provide, but in any case, make a donation for their help.
Research in Lebanon and Syria is difficult, but it can be done. The Jafet Library at the American University in Beirut, Lebanon, for example, is receptive to questions, and its staff will help if they can. If you know the Arabic names and the appropriate dates, you may be able to obtain birth and death certificates from district or central offices of the Bureau of the Census. Address your inquiry to the Census Office in the community (i.e., village, city, county) where your ancestor lived.
The Syrian National Archives staff in Damascus informed the author some time ago that birth, death and marriage records do not exist for Syria until very recent times, except in the parish records of various churches. Churches in many areas have survived the bombings; if you know the church your ancestor attended, contact it directly. Church records have not been catalogued, but they do exist. For example, church records for the Maronite and Armenian communities in Aleppo date back to the mid-19th century. If you can write your letter in Arabic or know someone who will write it for you, do that. If that is not possible, write the letter in English. Most areas have someone who can translate for the recipient.
The Syrian National Archives contains records of the various courts located in Damascus, Aleppo, Homs, and Hama for the years 1517-1919. The court records are a complete but rather confusing record of inheritance cases, property purchases, divorce proceedings, and other legal matters for Muslim, Christian, and Jewish urban populations. These records are not catalogued; given the lack of family names in pre-modern Syria, historical research on individual families is difficult and requires much patience. Syria's development of archival records is such that they may not be able to provide services for researchers abroad. However, I've been told they would warmly welcome anyone who came to Damascus for research. In that case, obviously, knowledge of Arabic or a good interpreter would be most helpful.
Keep in mind that the translation of names from Arabic to English often left much to be desired. Try to find out if the name you are researching has been changed; if so, you need to find out what it was in the Old Country before you can research abroad. As with other ethnic groups, there are names associated with occupations, i.e., Khoury/priest or Kaout/tailor; character traits or physical conditions, such as Eyen/sickly; or place names. A thorough investigation of the names you are researching is worth the effort, and will save time and money later.