Prep: Scoop Greek yogurt onto the center of a large cheesecloth or onto a few paper towels. Wrap so Greek yogurt is completely encompassed in the cloth, and set into a mesh strainer.
Strain: Set strainer over a large bowl and place a heavy can or two on top to help squeeze out the whey liquid. Allow yogurt to strain for 1 to 3 days in the fridge, or until liquid is no longer dripping out of the yogurt.
Flavor: Unwrap cloth and scoop cheese into a bowl. With a spoon or spatula, mix in olive oil and salt, adding more of either to suit your taste.
Shape: You can store this in log or ball form. For logs, shape cheese into a log, wrap in parchment paper, and store in the fridge. For cheese balls, roll yogurt cheese into small balls with clean hands. Store in a jar of olive or canola oil in the fridge.