The hydrogen peroxide found in many medicine cabinets for the
treatment of wounds behaves comparably to the bleach we add to washes.
When applied to blood stains, for example, peroxide liberates oxygen
atoms, which turns red blood pigments into less brightly colored
If you live somewhere sunny, spread the cloth in the sunshine and sprinkle water on the stain. Keep it wet and the sun will bleach it out. Depending on the strength of the stain, it may take a few hours.
This is the way our great-grandmothers did it. It has the advantage of being free and non-poisonous.
Maybe not as powerful as the way of @Shokhet, but anyway: try putting the clothes in a heavy-salted water for a half an hour. After half an hour, rub it with soap. Then wash out all the unwanted particles :)
OxyClean (or other sodium percarbonate based product) works so well. The sodium percarbonate in it, when mixed with water actually releases hydrogen peroxide (H2O2) and it also has soda ash in it which helps to boost the effectiveness of detergents and such.
I imagine the stain is quite dry by now. Here's some options I know work, to be used alone or consecutively:
Soak in cold water with a handful of salt, then wash as normal. (Optional: soak in bio detergent afterwards before using the washing machine.)
Cover the stain in a paste of bicarbonate of soda and water. Salt and water is also said to work, though I've not tried it.
As RedSonja says, the sun is magic. Put the shirt out with lemon juice or a lot of soap.
Ammonia is great for organic stains. Soak in cold water, 1 tablespoon of ammonia per litre.
Soak in water and bleach, or put a bit of bleach in the (cold) washing machine. The latter is less effective, but fine for removing faint stains.
General rule: cold water. Cold washing machine, if there's any stain left. Hot water sets blood. Would-be murderers, take note.
Don't mix ammonia and bleach. It generates toxic chloramine. You will die.
For future reference, if the blood is relatively recent:
Stick the stain under a cold tap and rinse until the water is running clear again.
Wet a bar of soap and rub it hard on the stain. I save the slivers from old bars for this: the sharp edges make it faster.
When you have a good thick lather, scrub the stain hard between your fists, cloth against cloth. Repeat steps 2 and 3, rinsing occasionally, until you think there's nothing more you can do.
By this point I've usually worked even very heavy bloodstains down to a faint yellow mark. Use one of the other methods to finish the job. (If you're going to wait overnight, put it in a basin of water so it won't dry out.)