There is a standard way that is used in the gem industry. The easiest way is to go out and buy a set of stone papers from a shop. Try gemology schools or even jewelers. If you want to DIY, then I will try to describe it to you. It's hard to visualize, but here goes!
1. OK, first you need a rectangular shaped piece of paper of medium weight. Like origami, we need to make some folds as guidelines.
Now, let's start!
2. Fold it so that you divide the length into 4 equal sections. Fold it again so that the width is divided into 3 sections, the center section slightly wider than the side sections.
With me so far?
3. Now open up the paper flat and position it on the table surface so that the bottom two corners of the width are closest to you and the length is perpendicular to you.
4. Place your gem into the FIRST fold and fold the paper up from the bottom. Then, fold in the two sides. Lastly, fold the last two sections of the width UP. And voila! Your gem is safely in your stone packet!
That wasn't too difficult huh? If you need a video, let me know and I'll try to post something on youtube! Hope this helps though!
I LOVE gemstones and am a gemologist.