The absolute first thing to do is,
find your oldest living relative and call them.
Most likely the first thing they will say is, "I don't have much to say." or "I'm not going to be much help."
Whether they know it or not, they are lying. They will be a much bigger resource than they realize.
The first question to ask them is, "Who is the oldest relative you remember?" Maybe they knew their grandparents, or even their great grandparents.
If all you can get from this relative is a name and a place where they lived, you can get started. You don't even need birth, death, or marriage dates. Just names and places will be enough.
Now you know who you are looking for.
Let's use my great grandfather as an example. Let's say that all I know is that his name was John and that my grandfather (his son) was born in 1910 in Utah. I also know that he died when my Aunt Bonnie was just a baby. She was born in 1941.
The next thing to do is visit familysearch.org
For information on how to register your free account, visit here.
This website has a huge database of historical records including censuses. And it's available at no cost to you.
Under the Search tab, I click on Records.
Next, I click on Residence
I'm going to type in John for first name, Buchanan for last name and then type in "Utah" and give a year range from 1910 to 1940.
Then I just click Search.
The next screen will show the search results. On the left hand side is a place where I refine my search or change any information that I want to.
The very first John Buchanan that appears best fits the description of what I know about my great grandfather. So I'll click on John Buchanan's name.
The next page will give me lots of information, thanks to volunteer indexers around the world. They read original census records and type the information into a database. Let's see what we can find out from this record.
1. In the 1940 census, John Buchanan is listed as being 70 years old. Most censuses were taking between April and June. So we can subtract 70 from 1940 and assume that John was born somewhere between 1869 and 1870.
2. Next we see that he reports his birthplace as Illinois. Now we have two new pieces of information. He was born sometime between 1869 and 1870 and was born in Illinois.
Let's scroll to the bottom of the screen.
3. We see that John is living with his wife. Her name is June Buchanan. This will be her married name. So we don't know her maiden name, but we can see that she was born 7 years after John, so most likely in 1876 or 1877. And we see that she was born in Utah.
In just a few minutes, I was able to get three new pieces of information about my great grandfather.
Hope this helps.