Peel cucumbers and slice very thinly using a food processor or a mandoline slicer.
Place in a medium-size bowl and mix in salt. Cover and refrigerate for several hours.
Transfer chilled cucumber slices to a colander and drain them for approximately 30 minutes. Squeeze the cucumbers or pat them with a towel to remove excess moisture. Either let them drain in the refrigerator, or refrigerate for at least 15 minutes after draining to re-chill.
Peel and crush garlic and mix with yogurt and vinegar. Add cucumbers to yogurt mixture and stir gently to combine.
Serve cold, with crackers, sourdough bread, or veggie sticks.