The first step is to learn, this article is not intended to give advise on how to handle different injuries or situations, there are a number of books on First Aid for Horses that you can aquire to help you with that. Some titles I found to be current, concise, easy to read, and cover the basics, include:

First Aid for Horses - The essential quick reference guide by Tim Hawcroft, 
Emergency -The Active Horseman’s Book of Emergency Care by Karen Hayes, 
Firstaid by Jane Holderness-Roddam.
Horse & Rider's Hands-On Horse Care : The Complete Book of  Equine First-Aid  by Karen Hayes, D.V..M.,

However you need to have a first aid kit put together that will assist you in caring for your horse in an emergency until a veterinarian can arrive.

No farm or stable should be without a means of rendering first aid to equine accident victims.
Equine First Aid is vital to the health and safety of our four-legged friends. Those of us working with horses have a  responsibility to be prepared for a possible emergency.

A first aid kit should contain both the  vital component of providing emergency care and those for just treating minor cuts and scrapes.  The contents of kits will vary, due to personal preference, but there are some basic supplies that should not to be overlooked. It is vital that you have first aid supplies close at hand. They should be kept in a handy and easy to access location. Familiarize yourself with the contents of your first aid kit and know how to use them. For the container itself, a plastic tool box with a tray on top is a  great way to transport your first aid supplies. Most discount stores have various sturdy plastic tool boxes that can be had at a reasonable fee. I have found that I prefer the bright red or yellow ones, so they are easy to locate. Just make sure it's big enough for all of your supplies. Take a permanent marker an BOLDLY mark FIRST AID FOR HORSES across the top, and each side of the container. This way if you have to send someone to fetch the container they are in no doubt that they have located the correct item. You may also want to have a more portable version, as it is a good idea to carry a kit with you when you are out on trail rides, horse camping, or are otherwise in a situation where veterinary attention is not readily available. Make sure it  is a waterproof, nylon bag with a zipper and covering flap make good choices. Make sure they have some means for attaching on a belt or a saddle. This kit would contain primarily emergency items that could help in the event of a cut or wound. 

There are also commercially packaged kits that can be purchased. If you are looking to purchase a ready made kit, be prepared to spend between $40.00 and $80.00 depending on what you are looking for. It's worth looking at what is available so you can find the one that suits you best.

The following  items are normally to be used only by or under the direct supervision of a veterinarian. When veterinary attention is not readily available, there are specific uses for each of these items, ask your vet for procedures
 

Hemostats	For use in a dire emergency with profuse bleeding from an isolated vessel and the hemorrhage cannot be controlled by direct pressure. These should be clamped directly across the bleeding vessel and should be left in place and bandaged over until a veterinarian can remove them.
Phenylbutazone	Bute is one of the most frequently used and abused drugs available for treatment of the horse. It is non-steroidal anti-inflammatory drug (NSAID) which is also an analgesic as a result of its anti-inflammatory action.  It is available as powder or paste for oral administration as a solution for intravenous injection and in some topically applied medicaments, in combination with dimethyl sulphoxide. The IV is very irritant if accidentally administered into the muscle or around the vein. If given intra arterially it causes death.  Consult your vet for administration situations and correct dosages. Ponies do not tolerate phenylbutazone as well as larger horses and are more susceptible to its toxic effects. Consequently smaller doses should be administered. Long-term use or use in very sensitive horses can cause irritation of the lining of the stomach and intestine and occasionally severe intestinal malfunction. Blood and bone abnormalities may also be associated with phenylbutazone therapy. The manufacturer states you can give an absolute maximum of 4 grams (2 grams for a pony) daily.
Acepromazine	This should only be used if your horse is so unruly or anxious that attention to the injury is not possible without some tranquilization. Acepromazine can cause collapse and even death under certain circumstances, so use this only if absolutely necessary.  Doses are administered at  3 to 4 ml (1 to 2 ml for a pony) in the muscles of the neck and wait 20 minutes for full effect. Sedation lasts for 2 to 3 hours.
Epinephrine	This should only be used when your horse has been stung by a bee or wasp or has received a vaccine to which he has had an anaphylactic reaction. If this occurs your horse will collapse within minutes to hours of being stung or injected. At this time you can inject 10 to 12 ml (5 to 6 ml for a pony) of epinephrine in the muscles of the neck or rump.

No one looks forward to haveing a horse injured, but the end results of the injury can often be minimized by the preparedness of the individual who is caring for the hores. 

What you can do: Keep calm and do only what is necessary while you wait for your vet. If you and the vet have worked together before, he may suggest a few additional things you can do, but don't start any treatment on your own and risk upsetting a delicate balance. You want your horse to stay calm; if his stall is convenient and he's calm there, place him in his stall and stay with him. 
If  he's the rare horse who's bled so much that he's showing signs of possible shock from fluid loss: shakiness, elevated pulse, pale mucous membranes in the mouth, he's better off outside on the soft grass, where he'll be cushioned if he collapses.

Make sure you provide your vet with concise information when you call.

What is the nature of the injury?
Where is the wound? 
How is the wound bleeding? In arterial bleeding, blood spurts out, venous bleeding is slower and more consistent
How recent is the wound/injury? 
If the horse is lame is there heat in the hoof and a digital pulse?
Age, Condition of horse (IE In foal?, Thin, Fit, Overweight)
Make sure you tell the vet the steps you have taken so far in treatment.

If your horse's feet are hot I would have someone squirt cold water on your horse's feet while you are on the phone to the vet. Some folks say this is a waste of time to help reduce or prevent Laminitis, but at worst you will have wasted some water, and Cold Hydrotherapy can be beneficial if you get to the horse BEFORE significant Lamellar damage has occurred. 

Take the horses temperature if illness is suspected, insert an animal thermometer into the rectum, and wait several minutes before reading. The normal body temperature of a mature horse at rest is 99^o to 101.5^o F. 

Check heart and pulse rates with a stethoscope if possible. These will vary with the age of the horse. Normal mature horses have a pulse of 28 to 40 beats per minute. Newborn foals have a pulse of 80 to 120; weanlings 60 to 80; yearlings 40 to 60. The horse should be calm, rested and relaxed to obtain an accurate heart rate. To determine the pulse rate, press your fingers against an artery. There are several locations on a horse where an artery can be felt, such as: (1) the back edge of the lower jaw; (2) the inner surface of the groove under the jaw; (3) inside the elbow, up and forward against the chest wall; (4) under the tail, close to the body; or (5) the inside or outside pastern. Practice is usually necessary to locate and feel the pulse easily. 

Check skin pliability for dehydration. Pinch a fold of skin on the neck and release it, it should quickly return to its original position. If the horse is dehydrated, the skin returns slowly and tends to stay in a fold. 

The color of the mucous membranes:  the gums, the inside lips of a mare's vulva, and the nostrils should be pink. A fire engine red color usually denotes illness. Anemia causes a pale color and lack of circulation causes a bluish-purple color. 

Rate of capillary refill (the rate blood returns to an area) indicates the quantity and condition of the circulating blood. Capillary refill can suggest anemia, colic, congestion and shock.You can determine capillary refill time by pressing your thumb on the horse's gum and releasing it. It should take about two seconds for the blood and normal color to return to the area. Longer capillary refill times indicate dehydration or a circulatory problem.