Tips and Advice on starting my search

I have just recently taken an intrest in my history after the birth of my son. My father refuses to give me the information I need to begin my search on our family's history. I know my grandmother is Norwegian and that she came over after 1910. He name is Elbie which is short for something like Elgiborge. I do not know her maiden name. This may be impossible to find anything about her. Hopefully you have done this before or have been in my situation. If you have any tips or advice on how or what I can do to find more information, I would love to hear for you. Thank you for your time.