Hire a professional art shipper if you are trying to ship a museum quality work. If you own an artwork by a famous artist, don't risk attempting to ship it yourself.
Have your artwork appraised, if you can. Shippers won't insure original artwork for more than $500 without an appraisal.
Clean the entire area where you plan to pack your painting.
Put on your art handling gloves before you touch the painting. Only acid-free, archival things should be in contact with the artwork.
Wrap the painting in acid-free, archival paper. Use several sheets of archival paper and wrap the painting thickly, just to be safe.
Tape the archival paper together with blue painter's tape. Make absolutely certain the tape has no contact with the painting.
Place the wrapped painting between at least 5 layers of stiff cardboard. This will keep the painting from bending in transit.
Wrap the cardboard up in either duct or masking tape. Wrap it tightly and apply tape all around the cardboard to prevent slippage. Wrap several layers around the corners to prevent damage.
Buy a box bigger than the painting from the shipper. Wrap the painting in bubble wrap, secure it with tape, put it in the box and put some "fragile" stickers on the box.
Buy insurance for the painting from the shipper. You may also want to send it certified mail. This costs extra, but because it requires an approved signature, you will be assured that your artwork will be delivered to the right person.