Eat everything you pick at least once, then mix the hell out of anything that the effects match for. Sometimes they'll surprise you and reveal new effects.
Is there anything in place that would keep you from accidentally re-trying something that failed before?
I'm wondering if I'm gonna have to get out a notepad and jot down all my failures, or it if will tell you that the particular combo will not work after showing that it wont.
The combinations should black out if you've tried them already.
For example, say this is your ingredients list:
Giant's toe
Thistle Branch
Blue Dartwing
Butterfly wings
Vampire Dust
Ectoplasm
Bonemeal
Creep Cluster
Nordic BarnacleAfter trying Giant's toe with Thislte branch and blue dartwing, you inventory would look like this after you click on giant's toe in the alchemy screen.
Giant's toeThistle Branch
Blue DartwingButterfly wings
Vampire Dust
Ectoplasm
Bonemeal
Creep Cluster
Nordic BarnacleThis allowed me to get all 4 effects out of some ingredients fairly quickly.
(also make sure to check what effects are unknown to you before trying a new mixture. Testing an ingredient you already have 4 of for new effects is a waste of time!

)
EDIT:
Oh, and the alchemy screen will also show the outcome of a potion if you already know it. So if you want to experiment with unknowns, go to the 'ingredients' tab instead of whichever effects you have discovered, and combine things until you get 'unknown effect' potions.