Use the wide holes on a box grater to grate the cucumber.
Add the grated cucumber to a thin dish towel, nut milk bag, or cheesecloth. Squeeze or wrap it tightly, and wring out as much water as you can.
Add the yogurt to a medium bowl. Add in the grated cucumber, dill, garlic, 2 tsp vinegar or lemon juice, salt, pepper to taste, and 1 tablespoon olive oil. Mix well. Taste for seasonings, adding more salt, vinegar, or olive oil as needed.
If possible, rest in the fridge for 15 to 30 minutes (or for several hours) to allow the flavors to marry.
If desired, drizzle with olive oil before serving.