Prepare your box and ensure it is taped well on the bottom, with the tape coming at least 1/3 of the way up the sides. This ensures tape is stuck in place and won't come apart from the box when lifted.
Use an appropriate sized packing box. Good sturdy packing boxes will be available from any reputable moving company.
Line the box with screwed up newspaper or a towel or similar.
Never use newspaper as ink will rub off onto your wine glasses.
It's best to use either foam wrap or bubble wrap for wine glasses. This provides that extra bit of protection.
Cut your chosen wrap into appropriate sized portions.
Gently wrap your wine glass, stuffing ends of the wrap into the glass and also making sure you wrap the stem.
Pack only wine glasses in the box. Don't mix with other glass or kitchenware.
Also use screwed up news paper to fill in gaps and to separate layers. This helps to cushion the contents of the box reducing the risk of damage during transit.
Never over pack your box, checking the weight as you pack.