If the labels says the food is trans-fat free, but the ingredients list includes partially hydrogenated oils, then you have to figure out how many servings of the food you're actually going to eat. If you're going to eat a whole bag of chips fried in partially-hydrogenated oil, then you're going to get some trans-fats. It's difficult, then, to know exactly how much trans-fat you're consuming, so it's best to choose products that don't have partially hydrogenated oils in the first place.
So what are partially hydrogenated oils, anyway? They're liquid polyunsaturated fat that have been treated with hydrogen molecules to create a semi-solid texture (like some types of stick margarine) and to improve storage time. The process changes the chemical shape of some of the fatty acids into trans-fats, which resemble saturated fat, except they're even worse for your health. Because of potential health issues, the amount of trans-fats must be listed on the Nutrition Facts labels, but as I stated, that can be a little deceiving.
United States Food and Drug Administration. "Trans-fat Now Listed with Saturated Fat and Cholesterol on the Nutrition Facts Label." Accessed February 12, 2008. http://www.fda.gov/Food/LabelingNutrition/ConsumerInformation/ucm109832.htm.