Use some loosely wadded newspaper under the lid or around the tone arm to keep it from swinging back and forth. Always unscrew the crank from the side and put it inside the machine. This keeps the crank from being damaged and also prevents loss. If the machine has a horn, remove it and pack it separately from the machine. These smaller instruments should always be shipped in an upright position.
Upright phonographs are a little more difficult.
If you are moving one and can keep it in an upright position, then the above instructions will suffice. Remove the turntable by lifting it straight up. Remove all the needles, the metal needle cups, and ANY other loose parts inside the record playing area. Secure the lid down by using a long piece of rope or a large elastic band and run it through the legs at the bottom, bringing the ends together and tying them at the top. Don't forget to remove any records from the storage area - the machine will be a lot lighter if you do.