Having an understanding of useful tools to apply to support an acute crisis or emergency, until veterinary attention is obtained can make a huge difference to the outcome in a critically injured animal.
The most important question to answer is "Is the animal stable?". This means that they are breathing regularly and normally and the colour of their mucous membranes (gums in mouth, some animals have black areas of pigment making it difficult to assess) are pink, they are conscious and responsive, there's no major pain or discomfort and there is no significant blood loss.
An unstable animal who doesn't meet one or more of these criteria is very likely to need immediate care. Ideally phone ahead to the vet with an outline of the situation so they're prepared and no time is wasted.
When an animal is unconscious or gasping and battling to breathe and their mucous membrane colour is white, purple or blue, check that their airway is clear. Pull their tongue forward out of their mouth and look for any obstruction such as a foreign object or vomit and clear it away or hold their head downward to help fluid to drain out.
If they are not breathing after you have cleared their airway then attempt to perform "mouth to nose" resuscitation by closing their mouth and breathing into their nostrils with just enough air to make their chest rise. Allow the air to be released and repeat every 10 seconds in larger dogs, and every 5 seconds in cats and small dogs.
An animal which is battling to breathe, despite a clear airway, is best positioned lying on their chest to allow their lungs to expand as easily as possible.
The next priority is to feel or listen for a heartbeat on the left side of the animal's chest, just behind their elbow. If there is no heartbeat then position the animal on its side and begin to massage the heart by compressing it with gentle but firm pressure on either side of the ribcage rhythmically between breaths. Check for a heartbeat every minute and stop compressions once the heart has resumed beating.
There are three very useful acupuncture points to which you can apply pressure with your finger nail or a blunt object to assist with resuscitation. These points are in the middle of the nasal plane in line with the bottom of the nostrils, the tip of the tail and the middle of the main pad of the hind feet.
If there is an obvious site of bleeding, apply pressure with a dressing or tourniquet. For an obvious fracture, use a splint such as a stick or block of wood bandaged on to stabilize the limb and in the case of a suspected back injury, transport the animal on a solid stretcher to prevent movement.
Keep the animal warm and dose Emergency Essence or Rescue Remedy. A couple of drops may be applied to the inside of the lip every five minutes until the animal is stable. Generally this works well and it is also often useful for the owner to have some too!