Preheat the oven to 400 degrees F. Place the salmon on a parchment-lined baking sheet and sprinkle with salt and pepper. Bake until the salmon is cooked through, about 15 minutes. Use a fork to flake the salmon and set it aside.
At the same time, steam the potatoes in a steamer basket over 2 inches of boiling water until they become fork tender, 13 to 15 minutes. Remove the potatoes and set aside. To the same steamer basket, add the green beans and steam until tender crisp, about 5 minutes. (Check to ensure there is enough water in the bottom pot at all times.)
In the meantime, whisk the yogurt, Dijon mustard, dill, lemon zest and juice, garlic and some salt and pepper in a small bowl until well combined. Set it aside.
In a large serving dish, arrange the cooked potatoes and green beans on a bed of arugula. Top with the flaked salmon and capers and then pour on the dressing.
Serve immediately or store in the refrigerator for 2 to 3 days. (If you're planning on enjoying this the next day, do not add the arugula until just before eating.)