How to do research
There are many websites with advice for beginners such as at the Family Tree website or Family Tree Magazine website.
Google "How to do genealogy research" for lots of advice, but be wary of hidden costs, freebies, or giving out information useable by identity thieves. Be wary of disclosing any personal information about living relatives.
Common sources of information include:
Interviews with family members. Also be sure to contact any other genealogists in your family.
Ancestry.com (Local libraries often have a free subscription if you do the research there and even have classes on how to use it. Ancestry.com has 17 billion searchable records and is the world leader in online research. Here is a list of some of the other better known online websites for researchers.)
Census records
Birth records
Marriage records
Immigration records
Naturalization records
Land records
Obituaries
Cemeteries
Newspapers
Old letters
Family Bibles
Church records
Military records
Listservs - especially the archives of listservs like the OCallaghan-L archives
Consulting other researchers
History Books - like Joseph O'Callaghan's book about the history and genealogy of the O'Callaghans
Archives, libraries, and book depositories
Don't be afraid of "Hitting the Brick Wall" around 1800. That's normal. At that point you can always start at the beginning in the 10th Century and move forward or get involved with a DNA project.