Tip 1: Grass-Fed Liver
First off, start with grass-fed liver. It's likely to be much more nutritious than liver from grain-fed animals, and the animals are treated better and raised in a more ecologically sustainable manner. It seems to me, moreover, that grain-fed animals have a mild form of fatty liver disease, on the basis that their livers appear yellowish instead of a deep, dark red as seen with grass-fed animals.
Tip 2: Get It Sold Frozen
Second, find a liver that is sold frozen. Liver spoils very quickly, and a liver that is refrigerated in a supermarket is probably already going bad. I have always preferred buffalo liver from North Star Bison, which arrives frozen and incredibly fresh. When comparing livers from beef, buffalo, lamb, and chicken, I like the taste of chicken liver best but find buffalo liver to be the best combination of taste and texture.
Tip 3: Keep It Fresh by Portioning
Third, aliquot the liver into portions you will use at one time to minimize the time it spends in your refrigerator. The best way to do this in my experience is to thaw it out for a few hours or however long it takes to be able to barely cut through it. It should only be partially thawed, and nowhere near completely thawed. Cut it into pieces that are just the right size that you will eat them in one serving. Put all the pieces back into the freezer in separate bags.
Tip 4: Soak It in Something Acidic
Fourth, thaw out one portion the night you are going to eat it. In the morning, marinade it in something acidic, such as lemon or lime juice. After it has marinaded for a few hours, slice it very thin and cook it in a pan with a little oil, flipping or stirring it frequently, for only one minute.
Tip 5: Add Your Favorite Flavors
Fifth, put whatever kind of nuances on this approach you want to make it more appealing. Add whatever spices you want or additional ingredients (such as sauteed garlic and onions, if that's your thing).
Why Does Freshness and Acidity Make Such a Difference in Taste?
For the chemistry buffs out there, I'm not sure exactly why these things work, but I think part of it is that liver is high in glutathione and other thiols, which are easily oxidized during extended storage and heating. I suspect oxidation of thiols contributes to the off-taste often experienced when eating liver. Acidic environments protect thiols from oxidation by keeping them protonated. Minimizing unfrozen storage and heat during cooking also protect thiols from oxidation.
Need an Easier Way?
What I've outlined here are the tips I've always followed when cooking my own liver. But I'll be honest. Right now I'm really busy and I need a sustainable way to get liver in my diet that requires less time. Currently, I buy US Wellness Meats liverwurst, which is pre-cooked and made from beef liver, kidney, and heart. It takes a lot less time to deal with, and it gives me a greater diversity of organ meats that provide a wider range of nutritional benefits. To learn more about how I incorporate this in my diet, check out my article, What I Eat.
Whichever route you go down, let me know how it works in the comments!