So you want to start a garden. Well, that's awesome, and you should feel nothing but encouraged. But then you see a stretch of back yard grass with your internet research on compost and hugelkulture and aquaponics in hand and think: "Wow. I actually have no idea what the hell I'm doing." Fear not, bud. Things aren't lost, and there's actually a really easy, cheap way to get into running a well-tended and fruitful garden.
Square foot gardening is fairly new, as ideas go, but has mostly come into popularity recently. The general idea is one of portioning your dirt into 1X1 sections and planting one kind of plant in that square. For numberphiles, these plants are always planted in square numbers like 1, 4, 9, and 16, according to the directions the seed packet gives for thinning out seedlings--that way, the spacing depends upon the adult plants and not wasting time thinning.
While SFG does usually recommend boxes and raised beds, it can work well even in regular old dirt if prepared properly. Also, while some folks generally recommend intensive use of fertilizers, there are more permaculture-oriented ways of going about it, including composting and clovering. For apartment dwellers, however, SFG is probably the best thing ever, since it means you can have a decent garden, even in a container on a small patio or balcony or next to a window.
So, SFG usually recommends you build a 4x4 box planter to make a raised bed. Why 4x4? No idea. Personally, I think they have a thing for square numbers. On the plus side, it does mean your beds are only so big that you can still get into them without needing to step in them or otherwise compress the soil, which is ultimately bad for the roots. You can also make the beds longer, but in general you want to stick with the 4' wide idea. It does make things easy. Usually, you see SFG folks doing this in multiples of 4, because they're just really into numbers, I suppose. (4x4, 4x8, 4x12, etc.) Having built the base bed, you then use wood slats or heavy duty string to make a grid of 1x1 squares, like graph paper full of dirt. The usual depth of these beds is six inches, but if you want to be really fun with numbers or grow root veggies, go for cubes! Cubes are fun. Like, an entire new dimension of fun.
Now, what usually gets used is a roughly equal mix of vermiculite (think pumice or a spongy stone that holds water and air), peat moss, and compost. Basically, you want a good loose soil that makes rooting easy on the plant and upkeep easy on you. The added bonus of the vermiculite is it makes the soil stay aerated and makes drainage easier, so the soil stays healthy. To be honest, though, I'd double up the compost. It's cheap, it makes for good soil, and there's no reason not to.
So you plant! If coming up from seeds, look at the directions on the back of the packet. After telling you how and when to plant, there will be a distance apart they want you to thin the seedlings to. Within a 12 inch by 12 inch square, these numbers will naturally lead you to squares of 1, 4, 9, or 16 plants per square. Plant that way. It's very symmetrical and suited for the OCD math and measures geek.
Then just water, grow, and harvest when appropriate. Weeding is fairly simple, since you know exactly what belongs where, and since the tight intensive spacing means weeds will have a hard time getting started once your plants have taken hold. Of course, you can also just mulch the soil after your seedlings have taken hold, and that'll make it even easier.
Ideally in a square foot system, you're watering the roots and not the plants. Some plants just aren't into water on the plant leaves themselves--like, say, tomatoes--and it's more efficient to water the roots, anyway.
One fool proof way to accomplish this without building a drip irrigation system is to just use soak hoses in a meandering line, running along the lines of the dividers. Or, if you prefer, you could set up a PVC drip system along that grid instead of even using any other dividers. Either way, you're providing water without soaking the soil the roots are in, and you're encouraging the roots to radiate out.
You could, alternatively, build ollas as resevoirs, glueing together unfinished terra cotta pots and planting them at the intersections of your grid and keeping them topped up with water to slowly leech out into the soil.
Or, you could even use a watering can. It's all up to you on how high or low tech you want to make this. The real benefit for overthinkers and tinkerers is that SFG makes all these nifty systems modular and easier to set up.
A lot of plants do well in a square foot system, especially herbs and veggies. In general you want to avoid perenniels and bushy varieties, but otherwise you're all good. Vine (aka indeterminate) tomatoes, cucumbers, even melons of some sorts all work well, provided you give them something to grow upward on and not outward on (like a string or sturdy cage) and keep all of their growth to one central vine--which, actually, is the best way to do it, since they'll produce more that way, anyway. Similarly, bulb veggies like onions and garlic do great in a SFG, as do carrots and all kinds of herbs. Leafy veggies like lettuce and cabbage and spinach also take well to it. Basically, you can get a really nice salad garden going if you do a square foot garden right.
One key thing to planting in a SFG is knowing how to space and how many to plant in each square. There are a ton of websites with recommended spacing, but in general you'll get your information off the seed packet itself. An exhaustive list of what you can grow is really not appropriate here, but let's just say you can grow anything you want, generally, as long as you're smart about it. If the packet says one plant every six inches, that's four plants per square. The math goes on from there.
Another key thing is knowing when to plant what. For this, you'll want to hit up your local agricultural extension service. For folks in Louisiana, that means the LSU AgCenter, which has so many docs and so much information available that you can literally exhaust yourself asking questions. One handy tool you'll find online is SproutRobot, which will give you a full planting calendar by zip code. In general, you'll want to a) wait until after Easter to plant anything outside, to make sure you're done with snap frosts and b) plan what you're planting out ahead of time so you can get a good idea of what goes in when.
Whatever you end up planting, it's good to start a lot of your plants off either in a seed sprouting box or as purchased seedlings. Before planting, you'll want to harden up your plants by gradually introducing them to the weather conditions of the real world. Generally, start a week before planting by putting them outside on a porch or in light shade for an hour the first day, two or three the next, and so on. This helps with the "So I just bought these plants, put them in the ground, and they fell over and died" problem.
SproutRobot Enter your zip code, it tells you when you should be planting things. Very useful!
SquareFootGardening.org A site that seems to be in limbo, but has good (if old and oddly organized) articles and pics.
MySquareFootGarden.net A great site from a lady who's been doing this method and teaching it since 2008, with up to date web design and easy to navigate information. Very useful. Also, you can see how obsessively you can plan out this type of thing.
The LSU AgCenter's doc list for home gardens. There is a truly mind-boggling number of PDFs on here. If you're the type to not sleep because you find this kind of research fascinating, consider yourself warned.