Don't lay it on its side. Always keep the refrigerator standing upright as much as possible. This ensures that oil won't seep into the cooling tubes which can cause permanent damage.
Read the manual. Check moving instructions in your refrigerator's manual before you move. It'll highlight important safety tips and advice and warn you of potential problems.
Don't hesitate to call a professional. While it seems simple enough, refrigerators are heavy, awkward and moving them incorrectly can cause permanent damage. If you're unsure about moving it, call a professional mover. Or if you do move it on your own and find that it isn't working effectively in the new space, have a technician look at it.