If you don't have Greek yogurt, you can use plain yogurt. Strain yogurt until it has reached the thickness you want. Peel cucumbers, then cut in half lengthwise and take a small spoon and scrape out seeds. Discard seeds. (If you use the small seedless or European cucumbers with few seeds, you can skip this step.) Slice cucumbers, then put in a colander, sprinkle on 1 T salt, and let stand for 30 minutes to draw out water. Drain well and wipe dry with paper towel.
In food processor with steel blade, add cucumbers, garlic, lemon juice, dill, and a few grinds of black pepper. Process until well blended, then stir this mixture into the yogurt. Taste before adding any extra salt, then salt if needed. Place in refrigerator for at least two hours before serving so flavors can blend. (This resting time is very important.)
This will keep for a few days or more in the refrigerator, but you will need to drain off any water and stir each time you use it.