Grate the unpeeled cucumber using a box or other hand held grater. Remove the excess liquid out of the cucumber by squeezing it in a clean towel, or pressing into a fine mesh strainer. Alternatively can grate using a food processor or finely chop by hand into ¼ inch pieces.
Squeeze the liquid out of the cucumbers using a clean cloth towel, your hands or by pressing into a fine mesh sieve.
Transfer the cucumber to a serving bowl and add to it the strained yogurt, dill, lemon juice, garlic and salt. Stir to combine.
Drizzle with the olive oil and sprinkle top with the dill or mint. Can leave oil and mint on top or stir into tzatziki.
Let the tzatziki rest for at least 5 minutes to allow for flavors to come together.
Serve with fresh raw vegetables (such as sliced cucumbers, cherry tomatoes, celery) and with toasted pita that has been cut into triangles and brushed with olive oil.