Fit a large bowl with a strainer, leaving plenty of room for liquid whey to collect on the bottom of the bowl.
Line the strainer with 2-3 layers of cheesecloth, or a clean flour sack towel, or reusable cheesecloth.
Transfer the yogurt to the lined strainer, leaving about ½" of space at the top of the material used to line the strainer. Fold the material over the yogurt and place something heavy on it like a fermentation weight or a can of tomatoes
Strain for at least 8 hours, or 10-12 hours for a Greek-style yogurt. Stir once or twice to encourage an even consistency. Strain for 24-48 hours for a yogurt cheese that can be used as a cream cheese substitute.
Transfer the strained yogurt to a clean container and store it in the refrigerator for up to 2 weeks.
Transfer the liquid whey to a glass jar with a lid and use it in fermentation recipes, or baking recipes to replace water.