Canning is a BIG topic. Lots to cover. I don't want to write a dissertation, so I'll keep it condensed.
Preserving the food you have is often a much better idea that trying to find more food in the future, when much of it is out of season. Canning is a great method. One thing to consider: Canned food is not particularly portable, especially when you consider the volume you may need. A can of veggies to go with lunch, and another for supper, means 365 cans times 2 for well over 700 jars. That's just a simplified example to highlight quantities.
When we say "canning" we usually mean "water bath canning or steam canning in glass jars". Look for end of season sales, and many people give away old jars. Old solid glass jars with glass tops, wire bails and a solid rubber gasket are quite usable but don't buy them, even used. The gaskets are expensive and hard to find. If you get them free, great, otherwise, buy newer mason type jars. Lids are supposed to be single use only. I tend to example all used lids. If they are is pretty good condition, I keep them and toss em in a bag for potential future use. I always can with new lids, but should shit hit the fan, and I run out of new lids, I'll try reusing old lids. I would expect higher sealing fail rates.
Water bath canning; Suitable ONLY for high acid foods. Tomatoes. Vinegar based recipes, etc. NOT suitable for meats, veggies. Greatly simplified, jars are boiled in water for 10 minutes to sterilize, and lids are sterilized. Jars are removed, quickly filled with hot, processed food, lids are placed on, and the filled jars are returned to the water bath and processed for XX minutes, depending on the recipe and the size of jar. This does two things: It further sterilizes the food and jar, and it heats contents, including air. As contents are heated, a little air if forced out under the lid. When the jar cools, contents contract, and dome lid is pulled down under slight vacuum. It is canned and preserved. Water bath canning kills most bacteria, while acid levels prevent growth of a few other bacteria, particularly the one responsible for botulism. Water bath canning low acid foods can lead to botulism, and cooking canned foods contaminated with botulism will NOT make that food safe.
Steam/pressure canning: You can water bath can in a steam canner (just don't close the lid). You can also pressure can. Dump food into clean jars. Put on lids. place in canner, with some water in bottom., Screw on lid, heat until steam vents for 10 minutes. Place weight on vent, and wait for vent weight to move. Continue to process for XX minutes. TUrn off heat and then remove product after waiting an hour or two. Pressure canning uses higher temperatures than water bath methods, and these temps kills ALL bacteria, meaning this method is safe for even low acid foods. You can process veggies and meats.
Equipment: You need a canner . For water bath, this is just a big stock pot. For pressure, you need a pressure canner. I own and have used all sorts. Spend the money and buy an All American. They are worth it. Buy a big one. You can process a small batch in a large canner, but you cannot process a large batch in a small canner. And for SHTF purposes, you'll need to process large batches.
Book: Buy the Ball's Blue Book of Canning. lots of good techniques and recipes. DO NOT follow grandma's old recipes from the '40's. Lots of dangerous recipes back then.
You'll need, jars, lids, a jar lifter (sort of plier thingie you use to reach into hot water, grab a jar and remove a jar), and a lid lifter (magnet on the end of a stick). Also a wide mouth funnel. A couple hundered dollar investment in equipment will last a lifetime.
Fro