Bleeding from small cuts and grazes can be controlled by applying pressure to the cut using a clean, non-fluffy pad (preferably a sterile dressing, if you have one) and by raising the injured part.
Once you are sure that the cut is clean and that the bleeding has stopped, apply an adhesive dressing.
The cut should heal by itself within a few days.
(Extract from NHS Direct website)
Seek medical advice from your GP or NHS Walk-In Centre if:
You should also get medical assistance if you think the cut is not healing properly, or may be showing signs of infection. The cut may need to be cleaned and/or stitched.