When I visited the tire store a few years ago, I had the tire salesman inspect my tires to see if they needed to be replaced. I saw him use a small tool to determine the remaining tread on the tire (in millimeters), and from there he determined if the tire needed to be replaced based on the remaining tread. The measuring tool is called a tire tread depth gauge. In general if your tire tread is 4 millimeters or less you should replace your tires.
After seeing the salesman use the tire tread depth gauge I wanted to purchase one myself. It turns out a tire tread depth gauge is pretty cheap, you can get one for as little as $6. Here is a link to a tire tread depth gauge which you can buy on Amazon: ITEQ Tire Tread Depth Gauge, Smart Color Coded Tire Gauge, Tire Tread Depth Accurate Measurement Tool
Now that I have my own tire tread depth gauge I can check my tires on my own to see if they need to be replaced and don’t need to take the salesman’s word for it. The video below shows how to use the tire tread depth gauge.