How do I connect my family search account to the free ancestry.com site?
Maybe you are referring to the free Ancestry.com accounts for Latter Day Saints ?
Again, as with visiting FHCs, this does not give you free access to the entirety of the website.
However, since I am a not a Latter Day Saint, I don't know how to set this up.
In case your question is about setting up for DNA genealogy work:
The secret sauce is the tree. For that see this other Discussion: Conflicting tree info
Alternatively, if your question is about Partner Access for LDS members to Ancestry.com, start with the relevant "Join for free" link here: https://www.familysearch.org/campaign/partneraccess/
There was a time when this site let all members use those free to member website but now I can not find how to do this anymore
Here is a link to the Knowledge Article that will guide you through the steps:
If further help is wanted, please call us at 866-406-1830, and a missionary will help you.