Peel the cucumber if the skin is thick. Also scoop out the seeds.
Grate the cucumber.
Sprinkle a generous pinch of salt and leave it for 10-15 minutes.
Squeeze out the water from the cucumber.
Add cucumber, oil, garlic, dill, salt, pepper, lemon juice to the thick yogurt. Mix well and the sauce or dip is ready.
Notes
If you are using normal plain yogurt you may need about 1½ cups of it. Take a thin cotton cloth (I find using a man's hankerchief the best). Place the cloth over a strainer or sieve. Place the strainer over a bowl to catch the water. Pour the yogurt into the cloth. Cover it up with the cloth. Put some weight like a mortar and pestle or a small brick. This helps to remove the water from the yogurt faster.
Peel the cucumber if the skin is thick. Scoop out the seeds.
Be careful with how garlic you use. You want a subtle and not an overpowering taste of the garlic.