Start with either a backpack or container that is durable and water proof. You may want to have a designated area where you can keep contact information/numbers of your rDVM and your information as well. Keep updated rabies/vaccine information in there too. Your dog may have specific needs to him/her, but here is a basic list to include:

Disposable gloves
Absorbent gauze pads
Adhesive tape
Small towels
Cotton balls/swabs
Scissors with blunt ends
Tweezers
Alcohol wipes
Flash light
Betadine or chlorohexidine solution
Antihistamine–25mg benadryl
Petroleum based lubricant such as vaseline
Eye wash/eye lubricant
Collapsible water bowl
Hydrogen peroxide–do not induce vomiting without speaking to veterinarian.
Thermometer
Muzzle/leash
Nail clipper
Ice pack

These tools should be used in an emergency or if you are hiking with your pet and not in close proximity to your veterinarian. Once you and your pet are out of the woods/adventure then contacting and seeking medical attention is important for any on-going issue. Overall, have a fun time, but be prepared!