Peel and halve the cucumbers. Scrape out the seed, coarsely grate, and mix with 1 teaspoon of salt. Set aside and let stand for 10 minutes. Rinse the cucumbers and drain thoroughly, then mix with the yogurt. Peel the garlic and pass through a press into the yogurt mixture. Mix in the vinegar and olive oil, and season to taste with salt.
Serve the sauce garnished with coarsely grated or thinly sliced cucumber.