Spray paint comes in oil and acrylic or water-based forms, with the addition of an aerosol component that makes it sprayable. Therefore, there's no spray-paint-specific magic trick for removing it from fabric. Your success will depend on what type of paint you're dealing with, and how much time the stain has had to set in.
Catching It Early
Treating a spray-paint stain when it's fresh is your best bet for beating it. When water-based spray paint (like acrylic) gets on your clothes, get to a sink and some dish soap as quickly as you can.
Step 1: Remove excess.
Gently blot out the paint with a paper towel or cleaning rag to remove anything that has puddled, or that may drip.
Step 2: Get it wet.
Apply a hearty amount of dish soap to the stain, and hold the fabric under warm running water to completely saturate the stain and garment.
Step 3: Work it out.
Rub the stained portion between your fingers as you continue to hold the fabric under running water. Reapply the soap and repeat, as necessary, until the stain disappears and the water runs clear. Launder the garment as you normally would after removing the spray paint.
If the sink doesn't quite do the trick, blot the stain with a sponge dampened with a bit of nail polish remover, and repeat the rinsing process.
For fresh oil-based spray-paint stains, start by scraping away as much of the stain as you can with whatever implement is handy and disposable, such as a plastic fork or spoon, and then reach for the turpentine.
Set the garment stain-side down on a large, absorbent cloth, such as a thick old towel. Sop up some turpentine with a clean sponge, and dab the stain from the back -- for instance, if the stain is on the front of a shirt, dab from the inside of the shirt. Refresh the turpentine and repeat the dabbing process, changing out the towel as it becomes wet or stained. Once the stain is gone, rub the spot with regular laundry detergent and soak the garment in hot water overnight. Then wash it as usual.
When it comes to oil-based spray paint, removal of dried stains may not be possible. In this case, try brushing the dried stain with a wire or hard-bristled brush, then applying a paint remover to loosen the stain. Apply some dish detergent and run the stain under warm water. Then repeat the process, starting with the paint remover, until you work out as much of the stain as possible.
Consult the spray paint can, if it's handy. The manufacturer might suggest stain-removal tips, or recommend a specific type of paint remover for stubborn stains.
For light water-based spray paint that has dried, saturate the paint with heavy-duty laundry stain remover, applying the product to the back of the stain. Allow the stain remover to set in for at least one minute, or as recommended by the manufacturer. Rub in a bit of heavy-duty laundry detergent, and then put the garment in the washing machine by itself, using the "stain" or equivalent cycle.
For bleach-safe clothing, soak the garment in chlorine or oxygen bleach for about an hour before laundering.
Even with acrylic spray paint, dried stains may not come out completely. Whenever possible, try to catch the stain while it's fresh, or use spray paint while wearing work clothes.