Yes dear readers, there is a right way to transport a refrigerator from point A to point B and the best advice I can give you is "no". Have someone else do it. Whether it's a moving company, the company you bought a new or used one from, whatever.
The second best option is that this must be in a pickup truck, trailer so it can stand up. With that, you must have it strapped securely or you will have it tip out on you. I had this happen to me with my personal vehicle 10 years ago and the ramifications were far from life threatening, but it could have ended really badly. It doesn't matter whether you're moving it a block or across town; SECURE IT. Ratchet straps work great for this. If you aren't sure how to do this, get someone to help you or have someone else move it.
The third and final option is to have this laid on its back to transport. If you have a station wagon or van this may be your only option short of hiring a contractor to do it for you. Personally, I've done it and never had a problem, but you must take something into consideration first. As you probably don't know, there is a pump at the back of every refrigerator (unless you own a gas one, then you should NEVER tip it). and connected to it (even the high end ones like LG and Samsung) are a filter dryer, a capillary tube as well as tubing going to two or more coils. Inside of this system is a gas called refrigerant that soaks up the heat inside the refrigerator with one or more evaporators and throws it outside with the help of a fan and the condenser coil.
Problem is that the pump, which is called a compressor, also needs oil in the worst way. The oil lubricates the valves, pistons, or other working parts to keep them from having an untimely death. This is not unlike the motor oil in your ride. If you tip the fridge on its back, oil will travel from the compressor to these coils from the compressor. While this isn't harmful in itself, turning the unit immediately after standing it up will cause problems with your system. The compressor could lock up and fail. Oil could still be in the capillary tube and plug that, as well as in other parts in quantities that it shouldn't be.
The best bet is to let it set long enough for that oil to drain back where it's supposed to be before you plug it in. A good rule of thumb is 24 hours, period. If you've just moved it, say from house to house on its bottom, it might not be a bad idea to let it set for a few hours as well. The oil is just oil, nothing special. However, it just needs to be where it can do some good. Contrary to popular belief, it won't affect the refrigerant or coolant. Again if you had to move this on its back, wait a full 24 hours to plug it in
As for moving them on their side, I've never done it and can't see how it would be any worse than on its back. My advice is not to do it though, as some units use condenser coils to heat areas inside the stiles (sides) and mullions (lintel or top) behind the doors to keep moisture off the cabinet. Sometimes these are looped in ways that might not allow oil to drain back to the compressor easily, if at all. So go ahead, let it drain, then plug it in and enjoy those cold ones (I like PowerAde myself). Don't forget to make sure the coils are clean and the water lines are hooked up if you have them. If you have an icemaker, this will need to be below freezing to make ice cubes. Maranatha!