There are two packaging methods that keep paintings well protected: using bubble wrap and cardboard, or using custom-built wooden crates.
For both methods, remember to properly insure the piece if necessary and to clearly mark the box as fragile.
Tape the box closed, and put the address on the label. Affix the shipping label to the box and place some tape over the shipping label so it does not accidentally get pulled off during shipping.
Use a custom wooden crate for artworks such as sculpture, large-sized paintings, and fragile items
You can attach a handle to the top or side of the crate to make transport easier. Use a cabinet handle from the hardware store and screw it into place. Make sure the screws are large enough to fit very securely; you don't want the handle to fall off while someone is using it to carry the crate. Don't use packing peanuts or other loose packing materials. They're a hassle for Buyers who have to unpack and re-pack artwork. They also settle during shipping, so they don't provide good protection.