FEDERAL CENSUSES (and mortality schedules):
From the census you can get get year of birth (by subtracting the person's age -- or age bracket -- from the census date) and sometimes the parents names, the state where the person was born, and the states where the person's parents were born. Census records are available on microfilm at the ten federal Branch Archives and at the larger genealogical libraries (SAR, DAR). Some censuses are becoming available on CD-databases. Some libraries may order a reel of census film for you for a reasonable charge -- but you have to know what you want (the indexes note the roll on which the name appears).
NOTE: When you copy a record, note on the back of the copy the year, state, microfilm roll, and frame or city, ward, and page (and note that some pages bear multiple numbers). You may make a pencil mark (ON THE COPY ONLY) to help the reader find your ancestor's name.
What's in the Federal Census? It has varied from one to the next.
1790 ORIGINAL WAS DESTROYED when the British burned Washington DC in 1812, was reconstructed from local records, names only the family head, indexed:
Whoa! What's a Soundex Index? It's better than a regular alphabetic index because the names are listed according to how they sound, and since census takers often mis-spelled names according to how they sounded, it is easier to use a Soundex system than to look up all the variants of spelling for Frey (Fry, Frei, Frye, Fray, Fries, etc.). We won't describe it here, but it is easy to get the Soundex codes for the few names you will be looking up. After that you don't need to worry about it.
The National Archives are in Washington DC, and there are ten Branch Archives are located in Waltham MA, New York NY, Philadelphia PA, East Point GA, Chicago IL, Kansas City MO, Fort Worth TX, Denver CO, San Bruno CA, and Seattle WA.
If you don't find the person in the index don't give up. Names were mis-spelled and left out of the index, but if you know the person's approximate address you can determine the census ward that they lived in and do a name-by-name search of the microfilm of that ward's census records. The records were generally taken in a house-by-house order down each street, and the streets are sometimes noted on the census forms, making your search easier.
What's the mortality schedule? This is a listing of all the deaths that occurred during the year immediately preceding the decade census year. Deaths in the other nine years are NOT listed. While this list misses 90% of the deaths, it does cover the other 10%, and that might have just the information you need.
STATE CENSUSES: Many states conducted a census in-between the federal censuses. These provide comparable information and are often overlooked.
Many of these census indexes can be found online at ancestry.com or footnote.com. If you do not have a membership, check with your local library, they may provide access to these services at the branch.