If using canned beans, go directly to the end of step 4.
If using dried, soaked beans, put the red beans, black beans, and cannellini in separate saucepans. Add four cups of water and one garlic clove to each pot.
Over high heat, bring each pot to a boil, reduce the heat to medium-low, and cook until the beans are just tender, about 30 to 45 minutes. Note: These cooking times will vary from one package of dried beans to another.
Using oven mitts or pot holders, carefully pour the liquid and the beans away from you into a colander set in the sink. Rinse with cool water, and then transfer the beans to a large nonreactive bowl and cover with plastic wrap. Refrigerate, stirring occasionally, until thoroughly chilled, at least 2 hours.
In a saucepan over high heat, combine the red wine vinegar, sugar, oil, salt, and the minced garlic. Cook until the sugar is dissolved, about 5 minutes. Transfer to a medium, nonreactive bowl, cover with plastic wrap, and refrigerate until thoroughly chilled, at least 2 hours.
Add the blanched wax beans, green beans, vinegar mixture, and onion to the beans in the large bowl and toss to mix thoroughly. Serve immediately or refrigerate in an airtight container until ready to serve.
YIELD: 2 quarts, serving 10 to 12
This salad is best if made a day in advance and will keep for up to 1 week if refrigerated in an airtight nonreactive container.