I would avoid using bleach for wound cleaning unless you are dealing with a necrotic wound (i.e. some tissue is dead). Dakins solution is mostly used in our days for really nasty cases of wounds, and you should already be in the hospital for this anyways. It was invented during World War I to deal with gangrenous wounds, since antibiotics weren't available back then. Probably the most common solution is half and quarter strength.

Caution: Dakins solution will dissolve blood clots and hinder wound healing.
Never use undiluted bleach on open wounds !
To make Dakins solution follow the formulas below. Dakins solution is not stable, so it needs to be used within 7 days of preparation, IF you add a pinch of sodium bicarb to it, otherwise prepare daily.

Dilute the following amount of bleach in 1 liter of water and add a pinch of sodium bicarbonate (baking soda)

solution strength : amount of bleach
full : 100cc bleach
half : 50 cc bleach
quarter : 25 cc bleach
1/8th : 12.5 cc bleach
1/16th : 6.25 cc bleach