Start by interviewing all your living relatives for birth dates & places, marriages, deaths, etc.
Look into local archives, church records. Then go on-line at FamilySearch.org, Ancestry.com, MyHeritage.com, Cyndislist.com. Where you go will depend on the country of origin of your ancestors.
Keep a careful record of your sources. You might have to revisit them when you come across contradictory information.
There are many free programs to record your information: Legacy, RootsMagic, Ancestral Quest.
