Heat milk over medium heat in large pot for about 15 minutes, until it reaches 180-185F (check frequently with an instant read thermometer). Do not boil.
Once the milk reaches temperature, turn the burner off. Slowly pour in 2/3 cup vinegar or lemon juice, while stirring with a spatula. Continue to stir slowly for about 1 minute, or until visible curds begin to form.
Let mixture sit for 10 minutes to slightly cool and continue to separate.
Line a sieve with damp cheesecloth (see note). Ladle larger curds into cheesecloth-lined sieve, and pour the remainder over the top. Place over a large bowl.
Let cheese drain for 10 minutes for very soft, wet ricotta; 30 minutes for a firmer, spreadable cheese suitable for most recipes, or up to 2 hours if desired. Season the cheese with a pinch of salt during draining if desired, taste, and add more if needed. The whey that accumulates in the large bowl underneath can be saved and used for another purpose or discarded.