They say that prevention is the best medicine. It is true. Do not take any unnecessary risks in any situation, be it in a remote or an urban setting.
Use common sense, know your abilities which will help you to make better decisions and therefore avoid problems. It is enough to not be able to avoid the unavoidable, but lets avoid what we can!
It is a good idea to go visit your doctor and dentist before undertaking a major trip of some sort, to be certain that all is well. If there are any problems then deal with them by following their advice. This would be better than heading out and suffering from a dental abscess as an example.
Once you are away from immediate medical care, you are on your own with whatever knowledge and resources you have on hand, both modern and natural.
For your own training go for a wilderness and remote first aid course if you can, but having standard first aid skills can still be of assistance. The reason for a wilderness and remote first aid course is that it is designed to teach you what to do when you are not in an urban setting where emergency services can be easily contacted. Have a look at the More Advanced Training section on the First Aid page for more info.
It is vital that you treat any injuries and illnesses as soon as possible to avoid further complications. Even a minor skin abrasion should be properly washed and dressed to avoid an infection. There isn't a large room for error in an emergency when you are in a remote area.
If you are in an urban setting when a major disaster hits it is equally important to take care of any injuries as soon as possible. You may not be able to have access to specialized medical care even if you are in a city when the disaster strikes, so avoid further complications by treating any wounds as best that you can.
Be certain to always have a first aid kit adapted to your needs and the trip that you are planning if heading out somewhere. At home do likewise as for all of your kits. Tailor your first aid kit to fit your individual needs. It is good to add Sam Splints and triangular bandages to your kit if heading out. Know how to use them as well as the items in your first aid kit, or what good will the kit be to you? It is preferable that if you are in a group that all have first aid knowledge.
It isn't recommended to head out solo, but it isn't forbidden. If you are going solo on a trip to a remote location, equip yourself appropriately and be very careful and alert. Bring along a personal locator beacon (PLB) just in case. There are varying prices as in many things. Have a look at this model if you are on a budget. It is a high quality portable PLB made by McMurdo. Have a look at the homepage for other PLB evaluations, and have a look at the companies websites who make them for their current models.
There are no guarantees in a serious remote survival situation, but you'll be on the right track if you take a wilderness and remote first aid course and take proper precautions and equipment with you, as well as having left a trip itinerary with a trustworthy person (or two). There are times that no itinerary was possible and you'll be subject to the conditions of that particular emergency scenario, such as a plane crash.
Prepare yourself as well for any emergency that may happen in your home town or in any other urban setting you may find yourself in if disaster strikes.