Peel the cucumber and slice it in half lengthwise to expose the seeds. With a spoon, scoop out all the seeds and shred the cucumber with the large holes of a box grater. Sprinkle a large pinch of salt (around ½ teaspoon) over the cucumber and set aside for 5 minutes to draw out the liquid.
In the meantime, mix together the yogurt, vinegar, grated garlic, olive oil, and dill until well combined.
Place the cucumber onto a paper towel or thin tea towel and squeeze out any excess water. Put the drained cucumber into the yogurt mixture and stir. If the sauce is too thick, add water to thin; if it's too tart, add more vinegar. Season to taste with salt and pepper, then serve with extra olive oil drizzled on top.
You can serve immediately or put in the fridge for half an hour, for the flavors to meld. The tzatziki sauce will last around 4 days in the fridge.