You can get a speciality Dinnerware box, which comes with a divider insert for your dinner plates.
For a regular box; get a small or medium box, tape it securely and line it with bubbles wrap.
Get a stack of packing or butchers paper
Place 1 plate on the stack in the middle of the paper and fold the sheet over the plate. If your sheets are larger you can carefully place the plate at one end and fold the paper over, place another plate on top of the first and fold over remaining paper. You can use sticky tape to secure the paper together if necessary.
If you dinnerware is fragile or valuable you can use bubble wrap or foam wrap. Wrap individual plates separately.
Place the plates inside the box on their sides.
Avoid over packing. Check the weight of the box as you pack, this is why smaller-medium sized boxes are advised when packing heavier items.
Once the box is full, line the top with more bubble wrap or screwed up newspaper.
Securely tape the lid of the box.
Clearly mark with "Fragile" and "This Way Up"