History girl goes back to school

I have spent many, many hours (willingly) listening to my Dad talking about his childhood, but it wasn't until more recently that I realised that he knew very little about his (and therefore my) family history. We're not talking ancestors of way back when here. The question marks start with the year his father was born. So, history girl, aka yours truly, moi, me myself, has decided to try and do some research, a little journey I plan to share with you. Not that I have a clue where to start. Modern history, what's that?!