Make sure your movers are adequately insured for personal injury, damage to the piano, and damage to the property at both ends of the move.
To move a vertical piano from room to room, carefully place furniture slides under the casters and slide the piano. Be careful with legs under the corners of the keybed, especially if they are not connected to the case close to the floor. If such a leg gets caught by anything, it might break and the piano might tip over. If the floor is carpeted, you will need a dolly that supports all 4 casters. Call your piano technician or piano movers. By putting the piano on a conventional mover's dolly, which extends only part of the width of the instrument, you risk the front of the piano tipping forward, the baseboard cracking, and the pedals getting damaged.
To move a grand piano within a room, have several people lift most of its weight and carefully roll on furniture slides to the new position. To move it through doors, call your piano technician or piano mover who will turn the piano upright, remove the legs and lyre, tie the piano to the grand board, and roll and reassemble it in the new room.
Even for the lightest spinet piano, I strongly suggest not to attempt to load it on a truck yourself. You and your helpers may get hurt and the piano will almost certainly get damaged. Keep in mind that taller consoles and upright pianos are as heavy as smaller grands, in the range of 700-800 pounds, and their weight is not evenly distributed.
It is best to hire fully insured, experienced professional piano movers. Contact your piano technician or a piano store nearby for references.
New federal regulations for trade of African ivory have been in place since July 6, 2016. See here for information on owning, moving, importing, and exporting of pianos that contain ivory. In a nutshell, musical instruments with African elephant ivory are subject to a de minimis exemption, but commercial activity is still severely curtailed or prohibited. Very old instruments may fall under the ESA antiques exemption.
Note that some states, such as New York and New Jersey, passed their own legislations that may supersede the federal rules.
If you plan to import or export a piano with ivory, the smoothest path may be to hire an import/export agent familiar with ivory-equipped pianos. Prepare all the documentation in advance. Based on the serial number, some manufacturers can provide a certificate of origin for the ivory they installed.
When moving the piano to another part of the country, your options are:
Your household moving company may offer to move your piano. They may even offer to prepare the piano for the move. Here's why those may not be good ideas:
Long-distance piano movers specialize in hauling pianos across the country, but not disassembling, packing, and reassembling them. They typically don't deal directly with piano owners, nor do they enter residential neighborhoods with their long trucks. Ask your piano technician and local piano mover who they use, and have them arrange the preparation, disassembly, packing, and long-distance move. You will need to hire a local mover on the receiving end as well.
Door-to-door piano movers will pack your piano, haul it to its destination, and reassemble it there. Inquire with larger piano stores, rebuilders, and piano wholesalers to locate such a mover. A disadvantage with door-to-door movers is that they may not be able to schedule the move quickly. Inquire whether their truck is climate-controlled.
To move a piano overseas, it will need to be crated and moved by airplane or on a ship. Hire an international freight company that has experience with pianos. Load the piano with double the normal amount of moisture-absorbing and moisture-releasing product such as Music Sorb, then wrap the piano with a moisture-insulating wrap.