Materials
You will need a whole red cabbage, preferably chopped into hand-sized pieces. You will need a mechanism to extract the juice, preferably a juicer, but a blender or food processor will suffice. You'll also need a quart of tap water, several cups for storage of the juice, plain white paper towels, a few coffee filters and several eyedroppers. You will also need several samples for testing, both with acidic and caustic natures. Lemons, vinegar and soft drinks make good "acid" samples. Baking soda, dry laundry soap and antacid tablets make good "base" samples. If you want to do more specific analysis, you can utilize cheap pH test strips to confirm your measurements.
Preparation
An important part of preparation is to ensure your audience that you are working with household ingredients. You can achieve this by taking a nibble of the red cabbage, a sip of the water, and offering a sample to those who observe. Add the red cabbage and water to the blender and blend until the resulting fluid is an indigo liquid. Use the coffee filters to remove the solids and pour the juice into several cups. At this point, you can take a sip of the juice to assure your audience that you are still dealing with nothing more than cabbage juice.
The Tests
Take a paper towel and tear or cut it into strips. Place a sample of each substance to be tested on each strip. For solid samples, mix them with some water and apply the mixture using an eyedropper. Take an eyedropper of the cabbage juice and apply a few drops to each strip. You should notice an immediate color change. The more acidic the sample, the redder the juice will turn. If the juice is applied to a base, the color will shift to blue and into green depending on the pH. For a more impressive visual display, you can add the samples directly to glasses of juice.
Analysis
If you take photographs of the color change of the cabbage juice in many samples and compare them to the pH of the final mixtures as confirmed by a pH litmus strip, you can create a surprisingly accurate measurement scale. To do this, you will need to use larger volumes of material and consistent measurements of the ingredients to ensure that your results are not skewed by experimental inconsistencies. Your photographic scale enables you to utilize the cabbage juice as a low-tech pH indicator across the entire spectrum of possible acid or base measurements.