Absolutely, positively not! The only circumstances under which a non-professional should move a piano is if you don’t care at all about the piano. If you care about the instrument getting from point A to Point B with no damage and playable, DO NOT TRY TO MOVE IT YOURSELF! It is dangerous to the health of the piano, but also to the health and safety of the people, to say nothing of the potential for damage to buildings and other property.
Yes, but that’s not the most important thing. You need three things to move a piano: equipment, strength, and knowledge. Too many people think, “All we need is four or five guys, and we can get this thing up those stairs, no problem.” The right specialized equipment is important, as is strength (I have seen my 800-lb grand picked up by two guys!), but the most important thing is knowledge. How to use the equipment, how to plan each step of the move, how to maneuver it so the least amount amount of lifting is needed (e.g., use of leverage, etc.) It’s not just a question of pick it up and go.
And you don’t want ordinary movers, you need a specialized piano mover. A standard moving company may say they know how to move pianos, but don’t believe them. On one of my cross-country moves, the company swore they’d have someone at the other end who knew how to unload and set up the 6-foot grand. When they arrived, none of them had ever done it. Fortunately, it was a simple move, with no stairs to speak of, and since I had seen it moved a couple of times, I could guide them through how to put the legs back on. But I was pissed to have to take that responsibility when they had said they would have an experienced person.
A good piano mover will charge a couple hundred bucks at each end, and if it’s a cross-town move, may not charge separately for the transport, just the loading and unloading. There may be additional charges over a certain number of steps, or if there are other challenges, but it’s worth it. If you value your instrument, do not skimp on this!