Slice the cucumber in half, lengthways. Using a spoon, remove and discard the seeds. Coarsely grate each half and place in a colander over the sink. Squeeze the cucumber to remove excess water and allow to drain as you prepare the yoghurt.
In a bowl, crush the garlic into the yogurt. Add the cucumber, lemon juice, olive oil, mix well and season with salt and pepper.
Just before serving, chop the mint or dill and mix through, adjust the seasoning if necessary.