I'm a believer in having well stocked first aid kits; both for people and for my dogs.
I'm so emphatic about this I have one each in my house, my car, my RV, and at my dog training business. Each has been used multiple times, from bee stings to cut pads as well as other injuries and minor illnesses. In the case of more serious injuries, having first aid supplies at hand allowed me to stabilize an injured dog until he could be transported to the veterinarian. A first aid kit has to be well-stocked, however, if it's going to be of use when you need it.
Phone Numbers and Records
Have a written record of important phone numbers in each kit—don't bypass this step just because you have them saved in your phone. A phone can be lost, damaged, or the battery can die. Write down your veterinarian's name, clinic name, address, and phone number. If they don't have emergency hours, what emergency clinic would you use? What if you are also injured? Do you have a family member or friend who can make decisions for your dog? Another number to keep on hand is Animal Poison Control Center (888-426-4435). There is a fee for information so have a credit card at hand.
Make sure you also have copies of your dog's vaccinations (especially rabies) and update these after each vaccination. If you've had titer tests done in place of some vaccinations, put copies of these in the kit as well. If your dog has some health issues, have copies of your pet's health record or details of the health problem in the first aid kit.
An up to date photo of your pet is vital should the two of you become separated especially in an emergency. Again, don't count on being able to use the photos stored in your phone.
Restraint Material To Prevent Panic Bites
Don't assume your well-loved, trained, socialized dog will never bite, because a hurt dog often will. Have a muzzle that fits your dog as well as a roll of gauze that can be used as a muzzle. Even an extra leash will work. Then every once in a while practice muzzling your dog; it's not fun of course, but better you know how to do this and that your dog not panic when you do. Just muzzle him, praise him, take the muzzle off and give him a treat.
Prescriptions and Medications
Have a week's supply of your dog's prescription medications and a written prescription for those medications in your first aid kit. In case of a disaster that requires you and your pets to evacuate, or if you're traveling out of town, you may not be able to get to your veterinary clinic. Having a week's supply will help you get through the first few days. A prescription will allow you to get additional medication if needed.
Bandaging supplies are the most used items in my dogs' first aid kits, so I keep a good supply in each kit. You should pack: rolled gauze of several widths (narrow and wide), non-stick gauze squares of various sizes, several rolls of elastic self-adhesive vet wrap, and several rolls of bandaging tape. Make sure you have a pair of scissors in with these supplies.
First Aid Equipment
This is a varied category and some of the supplies can be found at your drug store or pharmacy while others may be found at a pet supply store. The tools you need includes: scissors, tweezers, nail clippers, small flashlight, rectal thermometer (for pets not for people), needle-nose pliers, and stethoscope. Also needed are: cotton balls, alcohol wipes, non-alcohol wipes, styptic powder and styptic stick, KY Jelly lubricant, disposable gloves, and a small bottle of a grease cutting dish soap (Joy or Dawn are more widely recommended). Heat packs and cold packs are also good to have on hand. It's also nice to have a large towel or blanket that can serve as a sling to carry your dog.
Besides your dog's prescription medications, a few over the counter medications are important. A wound cleaner such as Johnson Johnson's antiseptic wash is good as is a triple antibiotic ointment for skin wounds. Sterile saline for washing eyes is important, as is an antibiotic ophthalmic ointment. Ear cleaning materials, include a solution and gauze pads. Ask your veterinarian which anti-diarrhea medication they would recommend for your dog. Always have some Benadryl on hand for bee stings and other allergic reactions (the dosage is 1 mg per pound of body weight). It's also a good idea to have a couple of tubes of Nutra-Cal or other nutritional support on hand, especially for performance sport dogs, hard-working dogs, puppies, and toy breed dogs; any of whom can suffer from low blood sugar.
Refresh Your Kit Twice a Year
I refresh my first aid kits when the time changes each spring and fall. I change my clocks, check my smoke detectors, and refresh the first aid kits. By following this schedule, I don't forget to do it. When you refresh your kit, replace anything that's been used or broken, check expiration dates, and look to see if anything has been taken out of the kit. Replace anything that needs to be replaced.
Talk to Your Veterinarian
Ask your veterinarian if there is anything specific they recommended for your specific pet in your geographical region. Not only does your vet know your pet, but they know any heath problems being seen in the local area, such a the canine flu or ticks carrying Lyme disease. If you're going to be traveling, ask about that area. Add those recommended items.
If you're not confident about your first aid skills, check and see if anyone in your area teaches the Red Cross Pet Emergency First Aid course (or a similar course). The Red Cross course is designed for pet owners and so is not overly technical, but it does give a good overview as to what to do in many different emergencies. It also includes a first aid book and a DVD; both of which can be useful references.