Summarize:

If possible, use your dill within a couple of hours. It will have the most flavor in this time period. For that reason, it's best to cut it right before you want to use it in your food. Try cutting dill with scissors instead of a knife when preparing it in the kitchen. It will be more flavorful. When looking at the plant, look for shoots going off the main stem at a perpendicular angle. Use small shears to cut the shoot about 1 inch (2.5 cm) or less above the joint. Cutting causes less damage to the plant, so it keeps it from decaying as fast if you're planning on storing it. Add 1 to 2 inches (2.5 to 5.1 cm) of water to the bottom of a mason jar. Snip off the bottom of the stems on the dill, and place the dill stem-side down in the water. Cover it with a lid, if possible, and put it in the fridge.  If a lid won't fit over the jar, use a plastic bag and a rubber band. Store the herbs for up to 2 weeks.
Use your dill as quickly as you can. Cut branches off the main stem when you're planning to store dill. Store dill in a jar in the refrigerator.