NOTE: While I use cheesecloth for this recipe, you can substitute coffee filters and adjust for the different material.
First, strain the yogurt the night before. To do this, line a colander with cheese cloth (a large piece doubled over). Put the yogurt in the cheese cloth and wrap it up with a knot on top. You can either leave the yogurt in the colander and put the whole things in a large bowl OR hang the bag of yogurt over a tall bowl or a large pitcher so it will slowly drip water out. I normally use large paper clips to fasten it to the sides of a large plastic pitcher. Let it sit like this, draining in the fridge overnight (at least 10 hours). In the morning, toss the liquid away.
The next day, cut the cucumbers lengthwise and scrape out all the seeds. Grate the cucumbers and sprinkle with 1 tablespoon of salt. Line the strainer with cheesecloth and lay the cucumber on it. Leave them in a strainer for about 20-30 minutes to draw out all the moister. Fold the cheesecloth up and squeeze them out well. You can also blot them with paper towels. Do everything you can to get all the liquid out of the cukes. The less liquid in the cukes and yogurt, the thicker the dip will be.
Now, in a food processor or blender, combine the cucumber, minced garlic, lemon juice, olive oil, black pepper, and dill until well combined.
Pour this mixture into the yogurt and mix well. Salt to taste.
REFRIGERATE FOR AT LEAST TWO HOURS. This is essential as it allows the flavors to mix. It won't taste right until it sits in the fridge. It's even better if you leave it overnight (the flavors intensify).