Wash and dry the clothes prior to using a Sharpie on them. Shrink the garments, because shrunken fabric threads are tighter and can therefore help prevent bleeding.
Insert a piece of cardboard between the layers of clothes. If you are drawing with a Sharpie on the front of a T-shirt, for instance, set the cardboard in between the front and back sides of the shirt. This will prevent the Sharpie from bleeding through the front to the back.
Draw gently on the clothing with the Sharpie marker. Don't press too hard or else the marker will start to bleed. You need only to barely touch the marker to the fabric in order for it to leave the design or words you want.
Do not get the area with the marker wet, or this will cause the marker to run and spread throughout the clothes.
Spray a stain remover spray directly onto the Sharpie spot and anywhere else that the Sharpie bled. The stain remover should deter the marker from bleeding any further and keep the stain in its place until it can be washed out.
Spray hairspray on the spot if you do not have a stain remover spray available. Hairspray can work similarly in that it holds the bleeding stain in place by hardening the fabric.
Press the stain with a dry rag. Blot the stain and spray with the rag, but do not rub the stain in. This will hopefully keep the stain in its place and soak up some of the marker ink.