Pour 1/2 gallon water into a large container or pot. Cover loosely and allow to sit for 24 hours to allow dissolved chlorine to escape.
Crisp cucumbers by storing in the refrigerator or soaking in very cold water for 1 hour.
Bring 1 cup water to a boil in a saucepan. Add salt and stir to combine. Set aside to cool.
Wash cucumbers in cold water and remove any blossoms clinging to them. Quarter large cucumbers lengthwise; cut medium cucumbers in half lengthwise; leave gherkin-sized cucumbers whole.
Peel and gently crush garlic cloves, but don't splinter them into fragments.
Pour cooled salt water into a 1/2-gallon mason jar. Add cucumbers, garlic, dill, and dried chile peppers, arranged attractively. Pack cucumbers tightly; they will shrink as they pickle. Fill the jar with dechlorinated water until cucumbers are just covered to avoid overly diluting brine.
Loosely cover the jar and set it aside at room temperature; set the jar on a dish if it is full to catch any dribbles. Let sit undisturbed until fermentation begins, 12 to 24 hours.
Refrigerate pickles in brine and loosely covered as they approach the pickling stage you prefer: new, half-sour, or sour. Don't overshoot the mark, as refrigeration slows but does not stop fermentation.