the best way to carry a monitor is no doubt in an aluminum or plastic transport case with the foam cut in the shape of the monitor. this can get expensive though.
a cheaper option would be to pack it in a stiff rectangular bag of some sort with cloth, packing material or other such padding stuffed inside.
the cheapest and bare minimum option would be to wrap the screen with bubble wrap and put the monitor in a box. you need to make sure you secure the monitor though since it doesnt have much protection.
depending on how long you plan on taking the monitor with you will change your transport plans. remember, unless the monitor is packed well any time you travel you risk some sort of accident. i've carried my $600 monitor before with...