Cut the cucumber in half lengthwise and use a spoon to remove the watery seeds. Coarsely grate the cucumber and place it in a sieve or clean kitchen towel.
Sprinkle the grated cucumber with a little salt and let it sit for about 10 minutes. Squeeze firmly to remove as much excess water as possible. This is important for keeping the tzatziki thick and creamy.
Add the Greek yogurt, drained cucumber, lemon juice, olive oil, minced garlic, dill, salt, and black pepper to a mixing bowl.
Stir everything together until well combined and creamy. Taste and adjust the lemon juice, salt, or garlic according to your preference.
Cover the bowl and refrigerate for at least 20 minutes so the flavors can meld and the garlic becomes more mellow.
Give the tzatziki a good stir before serving. If it seems thicker than you prefer, add a small splash of water or lemon juice.
Transfer to a serving bowl, drizzle with olive oil, and garnish with fresh dill. Serve chilled with warm pita bread, vegetables, grilled meats, or your favorite Mediterranean dishes.