Fennel can seem unwieldy to work with at first, especially if you buy it with the stalks intact. Once you cut off the stalks (slice them close to the bulb), you'll find you have a more manageable vegetable.
Next, peel the stringy fibers off the outer layer of the bulb with a peeler or sharp paring knife. Now you can cut the bulb into wedges and braise or roast it, or cut it into slices for sautéing or tossing with pasta.
1. Peel the outer layer to remove any tough strings. If it's bruised or seems very tough, remove it altogether
2. Remove the core for slices but leave it in for wedges -- the core will keep the individual layers together.