Firstly get yourself some professional packing boxes. You will also need proper packing paper or butchers paper. Both should be available from your chosen professional movers. Packing paper should come in sheets and this makes it faster and easier to pack your glasses.
Avoid news print as the ink can rub off on your drinking glasses. Instead use scrunched up news paper to fill
Tape the bottom of your boxes securely with proper packing tape. Tape along the length on the box as well as sideways, ensuring tape goes at least 1/3 of the way up the sides of the box, this ensure there is plenty of grip on the tape.
You can line the bottom inside of the box with screwed up newspaper or a towel.
Now to wrap your glasses. Place the glass diagonal at one end of the packing paper, and simply roll it up, much like wrapping fish n' chips.
Check the weight of the box, if it's not too heavy you can add another layer of glasses. Again use screwed up news paper or a towel to cushion in between layers. This will help avoid any damage.
Once you have sufficiently packed your drinking glasses, securely tape up the box and clearly label it FRAGILE.
Always use the appropriate sized box. Use smaller boxes for fragile items such as drinking glasses and never over pack the box.