First your living family members, particuarly your senior members. Tape them if they will let you. It might turn out they are confused on some things, but what might seem to be insignificant story telling might be very significant. People who do this state they go back a few years after doing research and listen to the tape again and hear things they didn't hear the first time around. Ask if anybody has any old Family Bibles.
Next your public library. They might have a subscription to Ancestry.Com you can use.
Ancestry.Com has lots of records and seems to be getting more all the time. They have all the U. S. censuses through 1930. The 1940 and later are not available to the public yet. They have U.K. censuses also.
Just don't take as absolute fact everything you see in family trees on any website, free or paid. Documentation is not required. The info is user submitted and mostly not documented or poorly documented. Also if a person has Family Tree Maker and a subscription to Genealogy.Com, for instance, they can merge other people's files into theirs and upload their merged files into various genealogy website. Unfortunately, Genealogy.Com encourages that. What that means is people are just collecting a lot of names for their database but don't really have quality research.
Documentation is very important.
A Family History Center at a Latter Day Saints(Mormon) Church has records on people all over the world, not just Mormons.
In Salt Lake City, they have the world's largest genealogical collection. Their Family History Centers can order microfilm for you to view at a nominal fee.
I have never had them to try and convert me or send their missionaries by to ring my doorbell. I haven't heard of them doing that to anyone else either.
Vital records, births, marriages and deaths are important. You can usually get parent information from them. The applications for a social security number I have seen and the death certificates also give the places of birth of both parents.
Rootsweb and FamilySearch.org(free sites) both have the Social Security Death Index.
You need the person's name as it was on social security OR their social security number. You don't need both even though there is a place for both. If you locate a person on the Rootsweb SSDI, off to the right is a block you can probe and it will pull up a letter for you to print off. Just put your name, address and relationship to the person, attach your $27 check and mail it.
Now in the U.S., each state has its own laws as to who, when and where a person can obtain birth and death certificates. Also, governing bodies (state, county,city) in many states were not recording vital info until the first quarter of the 20th century. Even once they started, a lot of people born at home or died at home did not get recorded.
If no birth or death records exist, you can perhaps turn to church records for Baptism, First Communion, Confirmation, Marriage and Death. Many faiths maintain these records and they often will have parent information.