Use the large holes of a grater to shred the cucumber. Then using a fine mesh sieve, squeeze out as much moisture as you can from the cucumber. (see ntoe)
Add the cucumber to a large bowl with the greek yogurt, dill, olive oil, lemon juice, garlic, and salt, and stir to combine. Check the seasoning and add more salt to your taste.
Cover and refrigerate this sauce for at least 30 minutes. (The longer it sits the better it tastes!)
Notes
If you don't have a mesh sieve, you can wrap the cucumber up in a few layers of paper towels and then squeeze out all the liquid you're able to.