There are various delivery companies in Japan, but Yamato (Kuroneko) is my favorite. They have an English version of their site with instructions on how to deliver your luggage to the airport, otherwise known as "Airport takkyubin." (Takkyubin is Yamato's special term for delivery.)
When I sent our luggage (two large suitcases weighing somewhere between 15-20 kg) off to Narita Airport last December, I simply called Yamato about 2 days before our flight, gave them my home address, told them how much luggage I had to send, and they asked for the best time to send someone for pick-up. I believe they came by that same day, and when the delivery guy arrived at the door, he gave me two slips of paper (the address labels) for each piece of luggage, on which I wrote our address, phone number, contents (i.e., clothes, etc.) and our flight information (don't worry, you can do this in English/romaji).
The woman I spoke to on the phone when I called Yamato spoke English, though I may have had to ask for an English speaking person (it was a year ago so I don't really remember that part). You can just ask, "Eigo ii desu ka?" (Is English ok?) or "Eigo o hanasu hito imasen ka?" (Is someone there who speaks English?) or something similar, if/when someone answers in Japanese.
The man who picked up our luggage spoke all Japanese, but the process is rather straightforward and they will simply give you the address labels to fill out. I dragged our huge bags (full of gifts mostly, and some clothes for padding, if you're wondering - we generally pack quite light) to the door for him to assess while I went and filled out the address labels.
After that, I handed them back, he gave me the receipts, (I paid too - cost less than 6,000 yen), we went through the whole "thank you" routine and that was that.
A few days later we arrived at Narita Airport, picked up our luggage at the appropriate counter, grabbed a luggage cart, and went to check it in.
It's all a pretty easy process, made easier by using English, and makes traveling by train much less of a hassle (assuming you have more than a backpack or carry-on).
You can check out Yamato's site and airport takkyubin here.
The online pickup request form can also be found here.
For more options, Narita Airport's website lists all the delivery companies that operate at the airport. I don't know if all of them have English speakers, so if you do try calling one of the others (or have done it before) in English, let us know in the comments. Of course, for those of you who can use Japanese no problem, take your best pick! (Though, I think most folks I've spoken with really like Yamato (Kuroneko)).
*And another tip, though slightly unrelated: IF you are traveling by shinkansen to Narita from south of Tokyo (typically via the Tokaido line), and going to transfer to the Narita Airport Express (NEX), do NOT transfer at Tokyo station. It's a big maze of a station, and even if you know it well, takes forever to make the transfer because you have to run through it, including the maze and the people. Instead, transfer at Shinagawa station (品川) - much, much easier.Happy, and safe, travels!
P.S. You can have your luggage delivered back to your home from the airport as well - no worries!