There are times when foods change how you absorb certain dietary supplements. Calcium carbonate supplements require stomach acid, so they're best taken with meals because food triggers production of hydrochloric acid. The other common form, calcium citrate, doesn't need the extra acid so it can be taken on an empty stomach. Vitamin D is important for optimal absorption of calcium, that's why it's usually included with calcium supplements and added to milk.
Iron supplements can be affected by foods and beverages too. Absorption can be increased by taking the iron along with vitamin C supplements or with foods or beverages that contain large amounts of vitamin C (like orange juice, peppers or strawberries). Milk or tea can interfere with iron absorption. This isn't a big deal if you're taking a little iron to ensure adequate intake, but if you're taking iron supplements to treat iron-deficiency anemia, you may need to be more carful. Follow the directions on the supplement package label or speak with your health care provider to make sure you're getting enough iron, while avoiding iron toxicity.
Dietary supplements also include herbs and other natural substances other than vitamins and minerals. Always follow the label instructions when you take those types of supplements.
United States Office of Dietary Supplements. "Dietary Supplement Fact Sheet: Iron." Accessed September 16, 2011. http://ods.od.nih.gov/factsheets/Iron-HealthProfessional
United States Office of Dietary Supplements. "Dietary Supplement Fact Sheet: Calcium." Accessed September 16, 2011. http://ods.od.nih.gov/factsheets/Calcium-QuickFacts/.