Step 1 is to interview all the living relatives (or even family friends) you can find for information on the family.
Be sure to keep notes on everything you learn and whom or where you learned it.
Now if you don't know any relatives to ask, and you want to learn information on your father, you will need to check public records. You can start with your own birth certificate. But don't forget to check your father's birth and death certs and your parent's marriage cert. If you know where your father died check for a newspaper obituary or death notice.