Working with one big handful at a time, lightly squeeze the grated cucumber between your palms over the sink to remove excess moisture. Transfer the squeezed cucumber to a serving bowl, and repeat with the remaining cucumber.
Add the yogurt, olive oil, herbs, lemon juice, garlic, and salt to the bowl, and stir to blend. Let the mixture rest for 5 minutes to allow the flavors to meld. Taste and add additional chopped fresh herbs, lemon juice, and/or salt, if necessary.
Serve tzatziki immediately or chill for later. Leftover tzatziki keeps well, chilled, for about 4 days