It's worth the money to invest in at least a small digital scale -- especially to measure flour for baking -- because cup measurements provide a much less accurate calculation. Weight produces an accurate measure of quantity, while volume can vary, depending on the air spaces between particles of an ingredient as well as how tightly you pack it.
But if you're caught without scales and need a quick set of conversions, you can make do by using charts, online converters or doing the math in your head. While for water, milk, yogurt and similar liquid ingredients, 8 ounces equals 1 cup, and 1 ounce equals 2 tablespoons, flour, for example, is only half as dense.
So 1 cup of flour typically is closer to 4 1/2 ounces, while a cup of granulated sugar is around 7 ounces.
If you're strong at math, you can write the cup measures in the margins of your recipe, changing 2 ounces of flour to 1/2 cup, 8 ounces to 2 cups and so forth. For more precision, take the recipe to your computer and work with online converters, which are especially valuable for specific flours including whole wheat, bread, all-purpose and rye.
These calculators account for slight differences in density for each type of flour. For example, the online flour converter at Traditional Oven finds that 1 cup of all-purpose flour is 4.4 ounces, while bread flour is 4.5 ounces, whole wheat is 4.2 ounces and rye is 3.2 ounces. King Arthur Flour also provides a table for converting between volume and weight in both ounces and grams. A site at Convert-to.com also provides numerous ingredient converters.
Check the inside flaps of your cookbooks for conversion charts from ounces to cups.
You'll do better measuring dry ounces in a set of measuring cups designed specifically for dry measures, which allow you to sweep the back of a knife across the top to level the ingredients, typically flour, sugar, cocoa and the like. Liquid measuring cups typically have a pouring lip and headspace above the top measure, and don't permit you to measure as precisely, since you can't readily level the top surface of the dry ingredients.