Prepare all ingredients in advance.
Combine oil and lemon juice in a medium mixing bowl. Fold the yogurt in slowly, making sure it mixes completely with the oil. Add the garlic, according to taste, and the cucumber.
How to strain the yogurt:
Line a medium-large bowl with a piece of cheesecloth or a clean white dish towel.
Dump a container of plain (unflavored), yogurt into the center of the cloth.
Bring the four corners of the cloth together and lift the yogurt.
Over the bowl or sink, twist the corners to squeeze out the liquid (it will drain through the cloth).
Place the cloth containing the yogurt in a strainer or colander, and place the strainer or colander in a bowl where it doesn't touch the bottom (so that the liquid can continue to drain).
Place the bowl containing the strainer/colander in the refrigerator and allow to drain for 2-3 hours.
Note: How thick is thick? The yogurt should be the consistency of whipped butter or cream cheese.
After dicing or shredding the cucumber, pat it dry with absorbent toweling to remove excess moisture.
The longer the tzatziki is refrigerated before serving, the more intense the garlic taste will become.