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Trim the ends of the zucchini, and slice them into ¼ inch thick sticks, 2 to 3 inches long.
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Pour the olive oil into a 12-inch skillet, and set it over medium heat. Toss in the garlic cloves, cook for a minute or so, until sizzling, and then drop the chopped anchovy into the pan. Cook stirring, another minute or two, until the anchovy melts in the oil.
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Scatter the zucchini sticks in the skillet, and toss and stir to coat them in oil. Season with salt, and cook about 15 minutes, stirring occasionally, until the zucchini are cooked through, limp and lightly caramelized. Finally, toss in the capers and cook another minute or two to blend the flavors. Serve hot or at room temperature.