Fennel mandarin salad
As it says, you chop the bulb - the white part at the bottom. The core of the bulb can sometimes be a bit tough, especially at the bottom, and you may have to remove the drier outer layer, but otherwise, that's the part you really want to use.

The bulb is juicy and easy to eat, while the green stalks are usually much more fibrous - think celery, except tougher. If you do want to eat the stalks fresh, you can try slicing them relatively thinly, so you don't have long strands of fiber to try to chew. Alternatively, they're great for adding flavor to soups and stews; you can just fish them out after they've released their flavor.