When the cardiovascular system can't get enough blood to your body, you will go into shock (and will probably experience low blood pressure and perhaps tissue damage as well). Heavy bleeding can cause this, but so can injury (i.e. piercing, cutting, suspension, and so on) and some peripheral events such as allergic reactions and serious infections. I have to emphasize that shock can be life-threatening; be prepared to do rescue breathing and CPR — you probably won't have to, but what if you do?
Because of that I strongly urge anyone who's working or playing in an environment where people could go into shock have up-to-date CPR and first-aid training!
A person going into shock will probably exhibit anxiety, look pale and have clammy skin and perhaps even bluish lips and fingernails. They may be confused, dizzy, and light-headed. They may sweat like crazy, have a rapid pulse, and exhibit shallow breathing. If the body is cold, raise the temperature. If the person is hot, lower their temperature with cold compresses. Of course, remember the old adage, "the face is red, raise the head; the face is pale, raise the tail."
If it's just minor, the person can normally recover just by sitting with their head between their legs, or by lying with their feet elevated; also, support people should be sure to keep calm (and keep "the patient" calm) since there's definitely a psychological component at work. If it gets to the point where breathing is difficult or the person is losing consciousness, the person should be put in the recovery position (i.e. lying on their side, supported by one leg and arm — the purpose is to widen the airway and keep the person from choking).
Your chances of going into shock are greatly increased by things like dehydration and heat; so if you're for example doing an outdoor suspension on a hot day, it's essential that you are well hydrated (ie. drink water or juice) and have a decent blood sugar level. If a person starts going into shock (but only in the very early compensatory stage), giving them something like Gatorade can often help to avert the situation — it should be emphasized though that many medical texts would strongly disagree with that advice because of choking/vomiting risks. If the person is wearing any restrictive clothing, it should be loosened.