We did this for a shower curtain one year:
DO IT OUTSIDE. It's messy!
SUPPLIES:
Spray paint in bright red.
Medical gloves (like what the doctors use - available from medical supply stores or beg your local doc to let you have a few pairs).
Clothesline/clothespins - string it up between two trees away from anything you don't want painted

and you might also want a few bricks as well to weigh down the bottoms of the plastic sheets.
Once you have everything, this is the fun part. Get your plastic pinned to the clothesline and stretched out so there are no wrinkles in it. Put on the gloves. Spray the can close to the plastic surface to simulate arterial spray (make an arc from the top to bottom), spray onto your gloved hands and grab the plastic or have someone on the other side to provide a surface so you can make handprints with your paint hand (flat surface behind the plastic so there's something to support the plastic when you touch it).
Spray more into your hand and flick your fingers at the plastic to get splatters and drips. Use old brushes (old toothbrushes that you're throwing out are great for this) and run your hands over the paint covered brush to get fine spray.
If you're careful, you could even save the medical gloves covered in red paint once they are dry - use them as props!
Our curtain turned out great, and once it's dry it stays put and only started flaking off about 3 years later... and mostly due to the fact that I folded it up for storage and it's flaking from the folded line parts.