If you've seriously thought about growing food to reliably displace some of the food you buy, and provide yourself with some degree of food security, the idea initially can be daunting, at least if you aren't a part of the tiny fraction of people left in society who actually work in agriculture.
Although I had some success with buying seeds from the store and growing a variety of different foods that way, I was concerned still. What happens when you can't just waltz into the local shops and buy a package of seeds? At one point I had a sealed up case of seeds that was supposed to last 5 years, but the rate at which the seeds successfully took off declined each year, and the package of seeds was expensive compared to the food I got. In the case of hybrid seeds, which seems to be most of the commercially available in larger stores, you can't actually harvest the crop itself for reuse the next season and that's if I had the skill and proper storage environment to store seeds in the first place.
I didn't. I was a newb at growing stuff, and my goal wasn't some kind of Home and Garden show backyard nicety. I wanted to field test if I could do something from start to finish on my own that if necessary could be scaled up to provide real food security. Ultimately I discovered the ultimate newb friendly survival crop, the potato.
Unlike other crops that are likely hybrids and won't grow if replanted, even store bought potatoes will serve as seed crop for planting. Potatoes eventually get “eyes” that are small growths out of the main body of the potato. These are the starting places of new potato plants. You can chop up potatoes into pieces with an eye and put them straight into the ground covered by an inch or two of dirt, a foot or so apart. For best results, with the eye pointed “up”. If that's as sophisticated as you want to get, you'll still end up with new potatoes in about 3 months. It's better if you allow the pieces to air out a few days and the exposed edges will “heal” a bit if you can wait before putting them into the ground. You can also plant the potatoes in a trench a few inches deep, then fill it up with more soil later. This is supposed to net you more potatoes.
Potatoes also come with a built in timing system telling you when it's time to harvest. The plant that grows up above the potato will turn yellowish and start dying back. This means it's time to dig the potatoes up. Usually this will start after about 3 months from planting. It can take longer if you planted potatoes without eyes, these potatoes will eventually sprout too, it will just take longer.
There are some other tricks to learn about planting potatoes. Don't plant whole potatoes. A healthy plant will sprout from a full potato, but when you harvest them you'll find a weird, discolored, and partially rotten potato with the other new fresh ones. You don't want to store these with the others, they'll just rot faster by being around them. Only plant a whole potato if it's a particularly small one. Golf ball size chunks with an “eye” socket or eye growing seems about right.
Potatoes also have a number of other advantages over other things you might plant in your garden. The 3 month turn around time means you can grow them quickly, and get in multiple harvests in the same year. Because what you actually eat is buried underground potatoes are less susceptible to cold weather if you plant them early or harvest them late. In this way you can sneak in days from the edges of winter with less concern. Even if the air temperature is freezing, the ground itself rarely freezes most places.
Another big advantage is the number of calories you get per space in your garden from potatoes. A lot of garden favorites like tomatoes just don't produce a dense amount of calories compared to the space they require, while potatoes can return 10 times the weight of the initial planted potatoes. My personal experience has been planting what fits in a small brown lunch bag and needed a five galleon bucket to haul in the harvest.
There's actually some security advantages to growing potatoes as well! It might be less common, but back in the day it was said that peasants preferred to plant potatoes because roving armies could burn fields of wheat easily, but since potatoes were underground, it took a dedicated force to stop and dig up the crops instead of just a random raider tossing a torch into a field. Your average unenlightened city-dweller probably won't know what a potato plant looks like (I didn't) while they might see fit to jump into your garden and help themselves of more obvious above ground growing crops.
A great thing about potatoes is you can simply replant what you have harvested. Just store them somewhere cool and dry and they should be fine to replant, even a season or two later. They also seem to be relatively hardy. I just water them occasionally, and hardly in a scientific way (Hmm, has it rained recently?). I like to plant multiple varieties, because one of the historical stories I know is of the potato famine in Ireland. It might just be wishful thinking, but different varieties might not be effected the same way.
Potatoes are just great food in general that you can cook many different ways. Baked, mashed, fried, plain, mixed with bacon and cheese, tossed in with your morning eggs (particularly if you have chickens too!) or any other methods you can think of. They are a staple crop and will keep you going.
Another thing to remember is to kill any fire ants nearby your potato patch. Apparently ants consider them food too! Good luck! I've already pulled one batch of potatoes out of the ground here in Texas and it's still just May.