Packing furniture is most of the time a problem. That's because furniture can be bulky and irregularly shaped. So the solution really is to dismantle the furniture. This is when plastic bags become very useful. Even the biggest parts of the furniture are packed in plastic so that they will not easily get scratched. If there are cushions and pillows, they are also put in large plastic bags so they will not get soiled or get dirty. It's just important that you seal the plastic well for maximum protection.
When dismantling furniture, you would usually remove screws. To make sure that you will not lose a single screw, you should pack everything in a smaller plastic bag. You should label it as to where it should be attached and what tools is required to attach it back. The legs should also be placed in a plastic bag, again, to protect it from scratches and damage. The bag of screws should then be attached or placed inside this bag so everything will go together.
The important thing is you put a cushion around the furniture parts before packing them. You should also cover them all throughout so they are properly protected. And of course, make sure that you will not lose a single part while moving your furniture.