Web merchants routinely leak data about purchases. And that can make it straightforward to link individuals with their Bitcoin purchases, say cybersecurity researchers.
Use blockchain explorers, like
blockchain.infoJust out of interest, I would like to take for example one of my purchases and see how much other purchases I can link.
As far as I know, there are companies that focus on blockchain analysis, with one of the most famous being
https://www.chainalysis.com/. They usually use their own software + standard Bitcoin Core nodes to gather information.
in most cases it is nearly impossible to use a block explorer like blockchain.info to analyze the blockchain and see where the payments come from and go to next.
and regarding chainanalysis, that is not a free service, and i don't think they just give anyone a demo. use
https://www.walletexplorer.com/ instead, it is the same company and it is free online tool.