The process is fairly simple, make a solution of:
80mg of potassium thiocyanate
10mL of water
3 drops of concentrated hydrochloric acid
5 drops of 3% hydrogen peroxide.
Shake up the mixture until completely dissolved.
Then get an iron nail and drop it in.
As time progresses, the nail will bleed.
What's happening is first the hydrochloric acid and the hydrogen peroxide are reacting with the iron to produce iron (III) ions. These ions then react with the thiocyanate ions to produce iron thiocyanate ions. These ions are a red color and give the appearance of blood. But since it only forms near the surface of the nail, it appears the nail is bleeding.