Well, I've lived in Japan for a year and now I'm getting the hell out. Time to graduate from college and return via JET or as an Eastern European stripper. That's not the issue though. I have never used any takuhaibin or general delivery services. No KuroNeko, nothing. How do you send luggage to Narita from the metropolitan Tokyo area? All I know is that it has to be done at least 24 hours in advance and that AmPm may be related. I searched the forums but to no avail.
How much luggage are you carrying? If it's too heavy to get to the airport by yourself, it might be too heavy to get on the flight. Remember that the airlines have weight limits, you might end up with an expensive overweight charge or worse, refusal to let you board. It could be cheaper to send some stuff back via postal service, like SAL or some other slow boat service. Check your airline before showing up with 250 kilos of luggage. Check the postal service for the special "book bag" rate to ship back heavy books and papers inexpensively. The book bag rate has been discussed in other threads here on FG.
These services are great if you want to avoid lugging your suitcase up and down train station stairs and on crowded trains on the way to the airport. You can have the takkyuubin pick it up at your home, or you can drop it off at some convenience stores (please check availability ahead of time).
If you want to use Kuroneko Yamato, this link will let you order a pickup online after you create an ID, but it's all in Japanese. This English language link lists phone numbers you can call to arrange pickup.
Just make sure you have a day or so before your flight and you know which terminal your airline is departing from. Go to your closest convenience store - 7-11, AMPM etc and fill in the forms. Send it to yourself, care of the terminal and mention the airline and flight number and date you are leaving.
The pick-up point is just inside the doors from the street on the departure level. Look for the company you used - most likely kuro-neko - hand over your receipt slip and take your bags. easy.
These days though, what I do is just get a cab to the nearest limousine bus terminal. Then it is just out of the cab and into the bus and then out of the bus. No nasty stairs or busy trains. Costs a bit more but it is really the most convenient I find. I am usually running late with packing so am not organised enough to send stuff by takkyubin to Narita. But I always use takkyubin when going on a ski trip as I can send all my ski gear 4 days before and have it be at my hotel when I arrive.