Drop the peeled bits into a bowl of acidulated water (water into which some lemon juice has been squeezed) immediately after cutting to prevent discoloration.
The vegetable's most classic employment is in the cold French salad celerie remoulade, in which the root is peeled, grated, "cooked" in lemon juice (or blanched briefly in acidulated water) to lose a bit of its rawness, then dressed with a mustardy mayonnaise.