There are a few basics to remember when it comes to finding your way out of the wilderness like finding a stream and following it downhill. This will keep you near a water source and take you out of the worst weather toward civilization. However if the weather is bad and there are no streams to follow you’ll need another method of navigation: the compass.
Modern-day survivalists aren't generally regarded as the most sane people on the planet. A quick look at any one of the disturbingly common and frighteningly thorough shopping lists they post online drives home the fact that anyone who self-identifies as a "prepper" most likely went off the deep end a long time ago. Sure, it's fine to keep a few extra cans of food and cases of water around for an emergency, but if you start adding body armor and butt paste to your stash, you might want to tell George Miller that it's time to see other people.
Hate to break it to you, but your dog probably has a better chance of making it through a total societal collapse than you do. A quick Internet search of "dog survives" lists everything from drowning to being shot, from bear attacks to war -- whereas the closest you've ever come to "surviving disaster" is getting your wisdom teeth pulled, and even then it was only with the help of a cadre of trained medical professionals and a carton of the strongest painkillers on Earth.
To me, the best option is to store emergency food. How much? If you have none, store enough for a few days. If you have enough for a few days, get enough for a week. How much you store depends on what time frame you think you're at risk for having to be completely independent. The early settlers of the southwest liked to store enough food for a whole year and still do to this day!