It depends what time your flight out is, but I almost always put mine out the night before. On most ships, they will give you colored luggage tags. Then they are sorted out by color, and you will go to the section with your particular color. Usually, it is pretty simple and works well.
If you have an earlyish flight where you are at all concerned about timing, it is worth it to carry them off yourself. Especially if they are easy to handle, but sometimes the elevators are jammed on departure day so you may have to do some stairs.