Generally, filing a mechancs lien requires filling out a specific form with project-specific information, presenting that form to the county for recording, paying a recording fee, then notifying the owner that the claim was filed. Still, the devil is in the details - and this article can help you learn the ins and outs of filing a mechanics lien in Tennessee: How to File a Tennessee Mechanics Lien | A Step-by-Step Guide to Get You Paid. This page has additional information about TN liens, as well: Tennessee Mechanics Lien FAQs.
Additionally, note that there are online service providers, including Levelset, who can help with lien filings. If you'd like to do that via Levelset, you can begin that process here or you can contact the team here.
As a final comment - keep in mind that the mere threat of a lien claim will often lead to payment without even having to pursue a lien filing. More on that here: What is A Notice of Intent to Lien And Should I Send One?