The quantities of this salad are really up to you, but I look for roughly 2 parts fennel to 1 part radish. When buying radishes look for those that are really firm. The longer, oval-shaped ones are really nice. Wash them and slice thinly. Fennel comes in two types: the thinner Fennel and a rounder, fatter variety. It is the rounder, fatter fennel buds that you want -- these are normally much more well packed, less stringy and generally have a lot more of the green tops, which you need.
Cut the tops and the excess stalk off the top of the fennel and set aside. Trim the bottom of the bulb in half and slice as thinly as possible from the root to the top. Put the radishes and the fennel into a bowl and cover with cold water, adding some ice. Leave for at least 15 minutes to get the radishes and fennel really, really crispy. Drain, spin them or pat them dry, put into a bowl and dress them with olive oil and lemon juice dressing. Chop the fennel tops and sprinkle them on top. This is great with grilled fish.