A stereotype of the survivalist is a person who stockpiles weapons, food, and various pieces of technology toward the end of surviving the End of the World as We Know It.
This may be accurate for a good number of such survivalists, but I can't help but wonder why they would take such a limited approach to survival. Remaining dependent on the technology of a world moved on, no matter how useful, is simply delaying the inevitable doom once the stockpiles have been depleted on the vain hope that a particular society will reassert itself. As such, it is probably not a good idea to keep many years' stockpile of consumables against the possibility of the collapse of society, for whatever reason.
There is one form of stockpile that one should have: Books. Information on how to prospect, gather materials, craft, cook, garden, repair, and do various things to survive and even thrive on their own power.
You see, books do not go away once used; they are not consumable, but limitless resources, depending on the care you take of your books. With the knowledge gleaned from the books, you can create your own technology, specifically designed with your needs in mind.
Speaking of technology, it is also a good idea to take a few hours, and troll the patent office records (usually online) in order to discover the kinds of technology you could find useful. While patents don't matter after The End, there are plenty expired patents you can use if you want to make a head start. Download copies of the patents in question, and store those against the day you may need to make use of them to construct your tools for survival.
So, what skills does one need for survival after The End?
The first, and by far the most important, ability to have is the ability to collect water. You can survive for days, even weeks, without food, but if you don't have a source of clean water, all the survival skills are useless. While this would justify one's stockpiling of water, it would be a waste not to gain that source now, prior to any possible need for water. That way, it won't be a big change when public water goes away.
The second skill needed is the skill of farming; the ability to plant and reap food is essential to survival. Food will not come immediately; it takes several months of appropriate weather for the food to grow from seeds to fruits, vegetables, nuts, roots, and herbs. It is also useful to keep some animals on hand as well, preferably for eggs and milk, although having the bare minimum to start breeding would not be a bad thing, either.
The third and fourth skills generally work together. These would be woodworking and metalworking. The former is important for the construction of many structures, as well as for carving the molds for the metalwork. Metalwork is essential for the creation of tools and machines; the ability to cast and machine metal tools and parts allows the survivor to make any possibly-needed tool for the purpose of dealing with issues as they come up. Together with woodwork, 95% of all things needed for survival is within reach of the survivalist without needing to stockpile.
Another set of skills that compliment one another are spinning, weaving, tanning, and sewing. The ability to produce leather and fabric and fashion them into comfortable clothing using homemade thread will be very useful in the days where clothing is no longer available at the local mall. Having clothing patterns on hand, as well as the ability to duplicate and/or modify them for your own unique physiology would be essential to making the clothing to the standards you are familiar with. In addition, having a crop of cotton can only help you in this endeavor. Of course, it would be important to have the woodwork and metalwork skills to make spinning wheels, looms, and needles for the creation of your clothing, as well as the frames used to stretch the hides for tanning.
Some additional skills would be the skills of glassmaking/blowing (the creation of water-safe containers and panes of glass for windows), masonry and stonework (the creation of foundational materials, as well as solid surfaces to work on), and some sciences, such as physics, mechanics (use of machinery to manipulate physics to your advantage), geology and metallurgy (finding and identifying natural sources of metals), and chemistry (helpful in extracting metals from ores and the creation of useful chemicals, such as cleaners, purifiers, and volatiles such as gunpowder).
In addition, after The End, you will no longer enjoy the (relative) peace of peace enforcement, meaning that you will need to know the skills to protect yourself and your family. Archery and marksmanship would be essential for the purpose of using the weapons that the above woodworking, metalworking, and chemistry skills would be able to produce.
Despite all this, one thing to keep in mind is that if it is at all possible, don't isolate yourself. Even if you thrive in solitude, there is always something to be said for being able to find someone else when that isolation becomes a burden rather than a comfort. More importantly, even if you have every one of the above skills, you may not be as good at them as your potential neighbors. And, of course, if The End occurs, it would probably be beneficial to find a way to make a New Beginning.
Will this guarantee your survival? Perhaps. It would depend on the quality of the place you find yourself in; an irradiated area would be a lot less likely to support someone than a fertile valley. Use your best judgement, and make the best of your abilities. Use the collected knowledge to keep yourself alive until either society reestablishes itself, or is replaced with another.
