There is a post on first aid for self harm here
cutting-self-injury/topic54211.htmlI will just add what I have learnt. (also possibly triggering)
If a wound is bleeding very fast you may have either cut or just nicked a vein, in this case grab some clean dressing/cloth/towel and use it to put pressure on the wound while keeping it elevated(above your heart if possible) don't try to peek at it for at least 20 minutes, if it bleeds through, add another dressing/cloth/whatever ON TOP of the original dressing and keep the pressure on. If you cannot control the bleeding after 30 minutes or is is spurting (spurting blood means you hit an artery, this is VERY serious) then you must go to the emergency room. It will be hard to tell your parents but explanations can be done later, they will be more concerned with making sure you are treated for your injury. If no one is around, call an ambulance. Your safety is the most important thing.
If you have managed to control the bleeding, you then need to see if you require stitches. Generally any wound where subcutaneous fat is visible can be stitched (if you see it you will know, tis little yellowish balls, very icky looking). If wound is gaping (ie: sides are far apart and will not stay together) then you may need stitches, only a doctor can be sure of this. Stitches are best done within the first 8 hours since the injury but can be done up to 24 hours after in some cases (the risk of infection is greater after 8 hours).
If you are sure you don't need stitches, then it's best to clean the wound (with antiseptic wipe or just rinse with water if nothing else available) and then apply butterfly stitches (these are thin strips of sterile tape used to keep a wound closed). They can be tricky to do yourself, especially if it is on an arm, but a doctor can do this for you if needed. Again it's best to do as soon as possible to prevent infection and scarring. Apply a dressing pad, bandage (not too tight) and change these every day (not removing the butterfly stitches) and try not to get the area wet.
Harm minimisation is important. Try if you can to stay away from cutting areas where the skin is thin/not a lot of protective fat such as forearms and ankles. Make sure that blades are kept clean in advance since you may not be of the mind to go and sterilise stuff when you are about to SH. Having a stocked first aid kit is helpful, things like antiseptic wipes, dressing pads in a few sizes, bandages, tape and butterfly stitches (or steri-strips as they are called here).