Look for a white, firm, plump bulb with no brown or yellow spots, with fresh green feathery leaves.

Allow 150 g or two small bulbs per person

It is best stored in the vegetable crisper of the refrigerator.
When left whole, it will keep for a long time in a cool place, though it tends to become woody as it gets older.
Freezing: only if cooked first 

The leaves can be used as a seasoning; the branches, or petioles, can be eaten cooked or raw like celery. 

The bulb can be steamed,

You can also blanch it for 5 minutes in boiling water, drain, continue cooking in butter, and finish it "au gratin."

In a pressure-cooker: leave the bulbs in for 10-15 minutes. They will retain their firmness.
Sweet fennel has a fresh, slightly licoricey taste which pairs well with vinegars, condiments, fish, cream, sour cream and court-bouillon.

raw in vinaigrette

braised in meat jus or in fish court-bouillon; perfect combined with tomato

boiled - peel and wash the bulb; boil in salted water or in a blanc [lien au lexique] for 20 minutes

marinated

Matches Made in Heaven
Bitter fennel has a slightly anise-like flavour. Sweet fennel has a fresh, lightly liqueur-like taste which pairs well with vinegars, condiments and fish, cream and sour cream, and court-bouillons.

Try eating fennel raw: it may come as a pleasant surprise! It is particularly tasty when combined with grapes or various flavours in a salad.

In salad - Peel the fennel bulbs with a vegetable peeler. Slice thinly on a mandolin. Soak in ice water. Drain, dry and toss with vinaigrette.

In butter to accompany fish - Sweat shallots and fennel in hot oil. Add some white wine and let reduce. Add some truffles, whisk in butter piece by piece, and season with salt and pepper.

Fennel can be cooked in sugar with star anise to make a filling for puff pastry.