Fronds: Reserve any feathery fronds that are in good shape to roughly chop and use as an herb or garnish.
Base and Stalk: Trim a thin layer off the base, usually less than 1/4" (5mm).
Then, cut each stalk off at an angle to cut as close to the bulb as possible.
Outer layers: If your fennel is pretty bruised, you may want to remove the outer layer completely. Either way, check underneath the first layer and rinse away any dirt, if needed. Reserve (or eat) any baby fennel bulbs attached to the base. To claim the outer layer:cut about an inch (2.5cm) off the thin wispy edges. Then with a vegetable peeler or knife, trim any part of the outside layer that is needed.
Cut
Halve: Cut the bulb in half lengthwise (from top to base).
Core: Stand each half on the cutting board, and while holding on to the top, cut in the direction of the cutting board a v-shaped wedge out of the tough core.
To Make Wisps
Set the halves face down: Thinly slice each half lengthwise (top to bottom) by hand, or with a mandolin. (Good in salads.)
To Make Wedges
Cut each half in half again lengthwise (top to bottom), then in half again into wedges. (Great simply served on a plate.)
To Make Thick Sections
Cut each half lengthwise (top to bottom) into 3 or 4 sections, around 3/4" (2cm) thick. (Great for caramelized fennel.)
To Dice
Cut each half lengthwise (top to bottom) (if you cut horizontally across the grain, they tend to fall apart) into about 6mm slices, leaving a little uncut at the stalk end in order to keep the bulb together while you dice.