It somewhat depends. If you are using it as simply a sweetener then you can replace a cup of corn syrup with a cup (equivalent) of artificial sweetener and a cup of water.
But often recipes call for corn syrup as a thickener, like in a pecan pie. In that case I would add a thickener, like guar gum or even cornstarch. But I must caution, one reason for using corn syrup is that as it cooks down it resists crystallization, you may not get the same consistency of results if that is the core reason that a recipe calls for corn syrup.