How do you prepare fresh fennel for cooking? My isntructions just say to "roughly chop", but don't say what parts of the plant to use.
Sometimes the outer leaves are a bit leathery (especially if the quality isn’t too god). When that’s the case I remove them first.
Next, I remove the green stalks – but Jefromi is right, the tiny leaves are delicious.
The kernel in the middle near the base of the fennel bulb is very hard. I usually cut it out by halving the bulb along its length and making two incisions with a sharp knife on either side of the kernel.
I chop the rest of the bulb so that it yields thin concentric slices.
It's hard to be absolutely sure without knowing what you're making, but since you say "cooking", it's pretty likely that you want to use the lower portion of the plant - the bulb. "Roughly chopped" is a good indicator that this is right. Those have a crisp texture, something like celery; they're good fresh and raw, but can also be cooked in a variety of ways.
The stems have good flavor but are pretty tough, like celery but much more fibrous. You can add them in big chunks to a long-cooking dish like a stew then fish them out. You can also slice them thinly, breaking up the fibers, and cook in plenty of dishes.
The tiny leaves also have a wonderful flavor, but like most fresh herbs, you don't want to cook them much; the flavor's delicate.