Search queries counter. How?

Question

Information Security

Good afternoon. I need advice from knowledgeable people, I decided to turn to this resource for help. I apologize in advance for the primitive and non-technical language in the descriptions.
I have a general idea about the operation of the following system:
a user enters my site, possibly fills out the form offered to him, then the site administrator has the opportunity to view previous requests in the search engine / browser of the person who filled out the form. There was a hint that a request counter (for example, liveinternet) could perform a similar function. Please help me and tell me more / give material for studying such a function, introducing it into the system and adapting the request counter.
Thank you.