Before you wade in.....
Dogs in fear or pain will bite. Even you, their owner! Use a muzzle.
Click here for a link on "How to make an emergency muzzle" if you don't have a proper one. But be careful, make sure it can be released quickly (tie with a bow) if the dog can't breath or vomits.
Cats can also be very aggressive when injured. Wrap in towel or coat to restrain and take to Vet.
An animal in pain or fear is already overdosed on adrenalin. If you're jumping about, screaming and shouting it's only going to make it worse. Stay calm, quieten things down and think.
Clear the Danger
Rushing into a road to help an injured dog is not a good idea: if the traffic doesn't get you the dog probably will!
Don't make the situation worse. Clear any overriding danger first. (e.g. stop the traffic, call for help, consider muzzling the dog).
Get some Help
If possible get someone to help. Handling injured animals is seldom a one person job.
If nothing else they can be phoning a vet for guidance and advice. Store your vets phone number in your mobile - now?
Basics, anatomy and resuscitation
In general, basic animal anatomy has more similarities than differences to human anatomy. Those with human First Aid training could do worse than apply similar rules when it comes to "what should I do?" The exception being human medicines which in many cases can be poisonous to animals. Click here for a a link about Dog & Cat anatomy
Both animals and humans need AIR via LUNGS to oxyginate blood and both need BLOOD circulated by a HEART to supply vital organs.
A lack of either is an immediate problem.
If an animal is breathing (note chest movement) you can assume its heart is beating and don't need to look for a pulse.
If the animal is not breathing you will need to check for a pulse (inside thigh or left of chest / heart).
Click here for link to "how to take dog's pulse."
If there is a heartbeat it may just be a case of getting the breathing going again by artificial respiration. This is done by holding the animal's mouth shut and breathing gently into the nose, don't overdo it; just sufficient to fill the lungs; note chest movement.
Click here for a link showing how to give artificial respiration and CPR.
If there is no heartbeat then you may need to carry out CPR (CardioPulmonary Resuscitation). See link above.
Note: Do NOT practice Artificial Respiration or CPR on a healthy animal as this can cause serious damage.