Select an ingredient at the top, and all matching ingredients are listed below. They are sorted by number of shared effects. Click a matching ingredient to expand or collapse the display of its effects (an asterisk denotes a shared effect). Limit results further using the effects checkboxes. Also, clicking-and-holding on a matched ingredient will make it the selected ingredient.
There are a couple of apps out there that provide similar information, but not in the format I was looking for. I personally use this mainly in the effects "discovery" process. No more eating herbs to learn the first effect (waste of an herb), and no more looking up multiple-effect-matches manually online.
Now I go through my ingredients with unknown effects, and with this utility I find the other ingredients that will reveal unknown effects using the fewest ingredients.
Learning all the effects is not necessary of course, since you can combine whatever you want to get the desired potion whether you know the effects or not. The main advantage in doing so, for me anyway, is having all ingredients listed under the appropriate effect heading in the alchemy interface. That way I don't have to hunt through the entire list of ingredients. I can go to the Fortify Enchanting section, for instance, and I know that I have all the herbs with that effect listed there.
NOTE REGARDING SPECIAL PERMISSIONS - The app as I wrote it doesn't require any special permissions; it doesn't do anything besides sort, filter, and display text. However, because I set it to be compatible with android v1.5 (by user request), Google automatically adds the requirements for "Phone Calls" and "Storage", presumably for compatibility with that older platform. You can take my word for it, or not, but the app doesn't use them.