Many indexes to births, deaths and marriages are now online. Libraries and family history societies usually hold further information. Purchase copies of certificates from the relevant Registry of Births, Deaths and Marriages. Death certificates of your immigrant ancestors will help you to find their parentage and their birthplace. Remember to check spelling variations of names and places.
Extend your research to electoral rolls, directories, cemeteries, schools, hospital and shipping records, naturalisation records, phone books and online databases.
Meet with fellow genealogists and attend talks on special topics relating to family research by joining local family history groups in the areas where your family lived as well as your state genealogical society