Add the ground coffee and cold water to a large bowl or pitcher. Stir to combine. Cover, and allow the mixture to sit at room temperature for at least 12 hours but no more than 24 hours. You may refrigerate, if preferred.
Set a fine mesh strainer over a large bowl, and place a coffee filter or several layers of cheesecloth in the strainer (see notes). Slowly, pour the coffee mixture into the lined strainer. The coffee will take some time to drip through. If using a coffee filter, you will have to pour in batches so as not to overflow the filter.
Once all of the coffee has filtered through the strainer, discard the grounds (or add to a compost pile). Store the coffee base, covered, in the refrigerator for up to 1 week. To serve, pour the cold coffee base over ice and dilute with water or milk as desired. A one-to-one ratio is a good starting point; feel free to adjust and/or add sweetener of choice.