it will depend on the recommendations of the supplement you are taking, so read the container first.
Some supplement labels tell you to take your supplement with food, which is very important because there needs to be a sufficient amount of real-food material into which the nutrients can be mixed and used by the body: otherwise, the absorption is adversely affected.
The most food-dependent supplements are minerals and mineral formulas, most B-complex vitamins and most multi-ingredient formulas like multivitamins. This also applies to Herbs as well. Taking these supplements without food can cause nausea, and malabsorption, or both.
The empty-stomach supplements include Ascorbate (the low-acidic form) such as Magnesium or Sodium Ascorbate, as this is a water-soluble Vitamin and best absorbed this way. You can also take higher doses of the low-acidic Ascorbate as it will not irritate the stomach which Ascorbic Acid has a tendency to do.
Fat-soluble and oil-based supplements (fish oil, flax oil, Co Q-10, Vitamin A, Vitamin D and Vitamin E) all need the presence of dietary fat for absorption. The products themselves often contain some oil or fat as a carrier for the nutrient, but this small amount may not be enough for complete absorption of the nutrient. So the directions will usually suggest taking these with food on the assumption that your meal will provide additional dietary fat.
But you don’t HAVE to take oil-based supplements with food apparently, since virtually all fat-digestion takes place AFTER it passes thru the stomach. People that I know of combine their fat-soluble supplements and take them all in just one or two doses, each of which could be taken with or without food.