You can research census records online through familysearch.com website for free. Find "catalog" in the menu. Put the state in the search box. Afterwards look at the menu on the right, look for census records in the menu and select the year you want. Once selected you will select the county your ancestors lived in. There is often a little magnifying glass on the right, select that and type in your ancestors name. It will show you all the people in that county with that name. When you find the correct person select him and the document should be there.
I like to use the FamilySearch.com site, since it's free. You can Google "Federal Census 1920" (or whatever) and one of the first results will be Family Search. Select that and you'll come to a search form to enter names and details. Good luck!
The 1950 US Census will soon be released to the public and will be transcribed and indexed faster than you can say jackrabbit. Previous US Census have been transcribed and indexed and you can do individual surname lookups at my favorites. Familysearch.org has them along with a whole bunch of vital records, worldwide. If you have money coming out of your pockets, you can subscribe to fee based on-line sites. But if you're cheap like me, head over to your local library and see if they provide access to the library editions of Ancestry.com and MyHeritage.com.
Keep an open mind that in spite of the best efforts, some people and families were missed. My Mom and Uncle Reese and some other family members aren't in the 1920 US Census. I believe there were quite a few as the Spanish influenza was keeping people distant.
But, say you can't find a maiden name for a family member? Whether city or country, a look-see for neighbors of similar age of your missing maiden names in an earlier census. If you see in the 1940 census your married male and no surname for the wife, look in the 1930 census or before if the marriage occured even earlier. And look around the block or the next farm or two over and see if one of the daughters with the same given name is there or missing from the even earlier census.
Every US Census enumeration district (ED) and supervisor district (SD) and maps changed over the years and familysearch has assembled them, but you have to associate a spot on one map to one ten or twenty years distant in time. Enough time for towns to change names or disappear.
Familysearch and Ancestry also include spelling variations, but don't rule out a search handing you nothing, learn the use of question marks (?) and asterisks (*), that would be another good question for the experts. I am not.
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You may wish to search Ancestry or FamilySearch for the U.S. Census. There may be a fee for using Ancestry. Instead, please check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
We hope this is helpful. Best of luck with your census research!
The only restrictions I know of are the age limits. The article says: "You must be at least 13 years old to create an account. Children ages 8 to 12 can create an account with parental permission."
If you can't use FamilySearch, another free option is to browse (not search) the microfilm rolls at the Internet Archive (archive.org). This is far from "the easiest way to search" as the original questioner asked, but if the computer index is defective, browsing can be the only way to find someone, so it is a useful skill to learn.
The tools at Stephen P. Morse's One-Step Web Pages can be a great help for searching and browsing. https://stevemorse.org/#us
If you’re looking for U.S. Census records, check with your local library to see if they have the Heritage Quest database. If they do and you’re registered with the library, online access from home should be free.
Also check your local library to see if they subscribe to Ancestry.com Library Edition. You can go to the library to do a search. Ancestry has also made the library edition available to registered library patrons using their home computer during the pandemic. I believe this is still available. You will need a library card and to be registered with the library for online access. See the library's website or call them to get more info.
While I use FamilySearch first, Ancestry is my go to second source. They have a different search engine than FamilySearch and I like their US Census images better because they highlight the name you searched on within the document so it is easier to find. As other users have said, both have good alternate name search engines and Ancestry can be somewhat customized. Even then you may not find your ancestor on first try as many non-English names were butchered in spelling by the census takers and even a good search engine will fail. Perseverance will be very helpful to you.
It is yet to be proven how accurate the index that NARA will provide. Given it involves artificial intelligence and OCR working with handwritten entries, I'm certain lots of cleanup will be needed. See https://www.archives.gov/news/articles/1950-census-access posted 14 December 2021 at the NARA News website.
