How is the "city directory" or "census" search done (for the layman)?
I use Ancestory.com for most of it. If you want to keep using it, there are fees involved. There is also familysearch.org
Ancestory.com seems to me to have the most to offer in terms of records. For some of the Lefever research I was able to pull census, city directories, even found Uncle Dan mentioned in a newspaper article about a state trap shoot. They also have Ellis Island records available. Birth and death records can be useful, if that is the type of research you are doing. Only a few city directories have come online so far. The data is similiar to the census, except in some locations they were updated yearly instead of the 10 year census period.
By law US Census records are public information. Having them in a digital format that is searchable key. More information is coming on-line, Canadian, British, German census, etc.
I found that the small village were my part of family came from has put marriage and birth records online going back about 200 years. So not everything is available on the mega portals.

There are others here that have more knowledge about these tools than I do. Hopefully, they will speak up.
Pete