Remove everyone from risk.
Calm the patient. This is far more important than you may think! Nearly all snakebites are successfully treated in the US. Most poisonous snake bites are not fatal. Panic only increases danger to the victim by increasing heart rate, and it spurs carelessness among everyone.
Use your snakebite kit immediately. The first few minutes are the most effective for venom removal. Follow the instructions provided in the kit.
Seek medical help at once. Recent studies indicate the single most effective thing you can do is calmly transport the victim to a medical facility. In most cases, severe complications DO NOT occur until several hours after the bite. If you're deep in the wild, make wise use of your time, but don't rush.
Remove tight watches, sleeves, jewelry, etc. Cut these items off if you have to. Note that rings and bracelets are especially hazardous as they will severely restrict blood flow to their particular extremity once swelling begins. Amputation is a likely outcome if these items are not removed.
While enroute to a hospital, apply a loose yet constricting band between the bite and the heart. This is NOT a tourniquet and should not be any tighter than a semi-tight watch band.
Keep the patient still if possible and immobilize the injured limb with a splint.
Treat the site like a puncture wound. If possible, wash the wound with copious amounts of soap and water. Once at the hospital, a doctor will likely give the patient a tetanus shot in addition to other treatments.
Keep the affected extremity at heart level or lower.
Avoid alcohol. It only increases metabolism and impairs judgment.
DO NOT GIVE ANTIVENIN IN THE FIELD! Many snakebite victims experience allergic reactions to antivenin and this potential requires that the person giving the antivenin must be ready and able to provide advanced heart and lung support -- something only available at a hospital via trained medical personnel, sophisticated machines, and powerful drugs. Further, more than six vials are often needed to treat one bite. More drawbacks come into play when the detrimental effects of heat and agitation (due to carrying the vials in a backpack) are considered.
Don't kill the snake! It was only defending itself and such an attempt may produce yet another bite.
Don't try to capture the snake -- it's not necessary. There are only two types of venom -- neurotoxin and hemotoxin (antivenin for pit viper bites is the same for all species). Based on the geographic area and the patient's symptoms, a doctor will usually know which type of antivenin to use.
NEVER cut an "X" at the bite site. This is ineffective and increases trauma in the area of the wound.
NEVER suck out venom with the mouth. The person sucking poison from the wound with his/her mouth will absorb the poison through his/her gums the same way a person absorbs nicotine from chewing tobacco. Further, the human mouth carries at least 42 species of pathogen† and this action could give the snakebite victim a major infection.
Don't excite the victim or allow him/her to walk if avoidable. Doing so will increase venom circulation.
Never apply a tourniquet, constricting band, or "Australian Wrap," unless you are well-trained in its use. As with snakebite kits, recent studies suggest this is of no help and even detrimental. (If, for some reason you do apply one, write a capital T (for tourniquet) on the victim's forehead AND the TIME you applied it. Relax it for 1 minute every 15 minutes.)
Do not apply ice, a cold pack, or freon spray to the wound. This does not retard the spread of venom.
Never apply electrical stimulation from any device in an attempt to retard or reverse venom spread. Studies show this does NOT retard or reverse the spread of venom.