Rinse the olives and separate out any with bruises or holes in them. (Olives with holes likely have olive fly larvae in them. Discolored areas may be another sign of affected olives, even if they don't have visible holes.)
Removing the bitterness
Smash or make cuts in each olive with a knife to help speed up the curing process. (Uncut olives will take at least a month vs. around a week.) If you have a lot of olives, consider trying out several different methods (slitting, smashing, and uncut olives.) Smashed olives are the quickest, but generally keep less time than slit or uncut olives. (Uncut olives keep the longest.)
Place the olives in a clean glass jar and cover them completely with filtered water. If you are making several batches using different methods, place them in separate jars. (Keep only smashed olives in one jar, slit olives in another, etc.)Some people add a small amount of salt to the soaking water, but it isn't necessary at this point.
Allow the olives to soak for 24 hours. Then, strain out the water and cover the olives with fresh new water. Soak for another 24 hours before changing the water again. (Continue this process, changing the water daily.)
After around 5 days, you can start to taste the olives for bitterness. Most people end up soaking smashed or slit olives for around a week, but that will depend on the size of the olives and how bitter you want the finished olives to be. Continue to soak the olives, changing the water daily, until you are happy with the flavor of the olives.
Brining the olives
Prepare a salt brine by combining around 55 grams (2 ounces) of salt for every liter (quart) of water. Stir well until all of the salt has dissolved. (You can heat the water to help dissolve the salt, but allow it to cool before pouring it over the olives.)
Place some of the prepared olives into clean glass jars and pour the brine solution over the olives. You can layer the olives with herbs and/or smashed garlic for added flavor. Popular choices here are rosemary and thyme.
Pour a thin layer of olive oil over the top of the brine solution, making sure to completely cover the water to keep air from reaching it. (No herbs or olives should be exposed or they may develop mold.)
Seal the jars and allow the olives to absorb the brine solution and be flavored by the garlic and/or herbs (if you've added them) for several days. Serve them when you are happy with the flavor of your olives.
Serving the olives
To keep the olives freshest (and keep them from softening too much), it is said that you shouldn't remove them from their jars with metal utensils or your hands. (I couldn't find the science behind it, but so many people believe it that I figured it was worth mentioning.) Ideally, use wooden or plastic utensils to remove the olives while serving them.
After removing all of the olives that you want to serve, make sure that the remaining olives are covered with brine and a layer of olive oil. Add more oil, if needed to completely cover them. Seal the jar again and store it in a cool dark place.
Video
Notes
This recipe has been modified. Many years ago, I cured the olives (removing the bitterness) directly in a supersaturated salt brine which I changed every day or two. I then placed them in fresh water to remove the excess salt once I was happy with their flavor. While that is a valid option, it does end up wasting some salt. I also received a comment that the recipe should be more exact. I have updated the recipe to reflect the method that I use now.
Seasonings
Apart from adding herbs and garlic to the olives, some people also add a splash of vinegar to their olives before pouring in the brine.
Storage
Store the well-sealed jars of olives in a cool, dark place (or a refrigerator). Make sure that the olives are completely covered in brine and that the brine is completely covered with a layer of oil before sealing them. (Any exposed olives or herbs may develop mold.)While the olives should keep well for many months (even a year or more), the flavor and texture will generally change over time. (They can get soft and overly salty.)
One-year brined olives
Another alternative to curing the olives and then brining them, try directly jarring them up in a more highly concentrated salt brine. This method generally takes a year to fully cure and brine the olives, but it's a great way to preserve them for longer periods of time if you have an overabundance of olives. To slow brine the olives, place clean, whole, unbruised olives in a large jar. Cover it in a brine made with 60 grams of salt for every liter of water. For every kilogram of olives, you'll need approximately 1 liter of water and 60 grams of salt.Completely cover the olives in the jar with the brine solution and cover it with a layer of olive oil to keep the air from reaching the olives. Seal the jar and leave it in a cool, dark place for a year! In a year, you can eat the olives as-is or further season them with spices and herbs!