First you need to gather all the information from your family that they know. Names, birth dates, death dates, places associated with them. Then go to FamilySearch, the LDS site. Search their site with every name you have listed, they have the 1880 census. Ancestry.com is having free access to immigration records till Dec 31. Each state has their own Genweb, some states are better than others. But go through all the states that you have ancestors that lived there and find what you can there. Cyndi's List is another site that can give you information.
If where you live, there is a local historical society, they have lots of information, books, microfilm, some online sites that they are signed up with, and they can also give you leads where to look for more information. They could also tell you if there is a close LDS library where you can get films, books, from Salt Lake City.
I hope you have a good printer, cause you will want to print off all the information you find on your family.
Watch out though, looking for information on your ancestors can become addicting, but it is so much fun. Not everyone understands it, but others that enjoy genealogy. Enjoy your adventure.