how do i remove blood from fabric without making a mess?

Cold water, never hot. Hot water cooks the protein into the fibres and then it's stuck. Rinse from the back of the fabric so you push the blood out rather than through. Then rub in some soap or bio detergent and soak in cold water for half an hour before washing. Old dried stains on white cotton come out with hydrogen peroxide, but it can bleach coloured fabric so test first.