Trim or cut ends from green beans. I do this by standing up a handful of beans, letting them fall down to the cutting board so ends are lined up, then trimming across the end with a knife; repeat with the other end.
Coarsely chop the Kalamata olives and mince the garlic.
Heat olive oil in a heavy skillet with a lid, using medium heat. Add the minced garlic and cook about 1 minute, just until the garlic is getting fragrant.
Add the green beans and stir until beans are all coated with the hot oil.
Add the canned tomatoes with juice, chopped Kalamata olives, capers, and 2 T water.
Reduce heat to low, cover the pan, and simmer for about 20 minutes, or until beans are just starting to get tender. I checked them and stirred a few times. If you have bigger beans, they will take a little longer to cook.
When beans are barely tender, remove lid, raise heat to medium, and cook until any remaining liquid is evaporated, probably not longer than a minute or two.
Season beans with salt and fresh ground black pepper to taste, and serve hot.
