Call 800-610-8734, say "Order supplies" and then ask for the Military Pack.  They'll send you six priority-mail large (12"x12"x6") boxes, tape, and labels, all for free.  They're marked "America Supports You," have a place for writing in the name and FPO/APO info, and are discounted $2 below the regular priority box rate.  Send up to 70 lbs to an FPO/APO address for two dollars less than the regular rate.  

You can also go online here and order cases of 10 or 25 online to have cases of boxes (no tape or labels) sent to you free.  Choose quantity under "select format" at right on that page.  Here's a good link to info, including addressing packages to FPO/APO addresses:  https://stamps.custhelp.com/app/answers/detail/a_id/774/~/overseas-...

You'll also need to complete a customs form for each box, available at the post office to fill out by hand, or complete it online here.  You don't need to get super-specific about the contents.  You can write the ship name or PSC and FPO info on lines anywhere under the recipient's name - here's a sample of the "old" form from a few years ago but the idea's the same :) 

From USPS.com:  

Inside Dimensions: 12" x 12" x 5½"
Outside Dimensions: 12¼" x 12¼" x 6"

Some key benefits:

• When used to send to APO/FPO/DPO addresses, $2.00 less than our domestic pricing.
• Box features the “America Supports You” logo and APO/FPO/DPO addressing block.
• Commercial Base prices are available for postage paid through Click-N-Ship service at usps.com, authorized PC Postage vendors, and other authorized postage payment methods, and the rate is even lower.
• The U.S. Postal Service offers free Package Pickup from your home or office at a time and place convenient for you. To schedule Package Pickup and for other pickup options and availability, visit usps.com.