There's a difference between natural sugars, and added sugars, though. It would be near impossible to find & eat '0' sugar gram foods, unless you stuck strictly to meat & eggs...
You don't want to be eating refined sugars... none of the white stuff added to the foods you're eating.
However, dairy products, tomatoes, fruits, veggies... they all have natural sugars in them. You'll see sugars listed on cream and half and half, on cream cheese, on cheese, on no-sugar-added tomato sauce...
What you want to do is avoid things with sugar listed as an ingredient on the label... and that includes all it's different forms (lactose, dextrose, sucrose, fructose, etc., etc., etc.)