Why and where you should build a square foot garden?

If you're already an organic gardener, you probably already have everything you'll need: space for square foot beds, fertile soil, compost, knowledge and experience. If you're a row gardener, these are permanent no-dig beds, no walking on them -- like raised beds, whether you build them raised or flush with the surface. If you're a raised-bed grower, use raised beds.
If you have a garden, but you're no expert, or new to growing food, first choose a good site. What makes a good site? Lots of sunshine, and tons and tons of that "well-drained, rich, loamy soil" the seed packets tell you to plant your seeds in, as if the stuff grows on trees. So just choose a good place where there's enough light, we'll fix the soil.

Take up a bit of lawn if you like, the soil under a lawn is usually quite good. Use a sharp spade to cut through the turf: make vertical cuts (use your foot), slicing it up into one-foot squares, then peel the squares off like a carpet. 

You only need to take off an inch or two. Pile the squares in a block, grass-side down, wet thoroughly as you go, cover the top with a garbage bag to keep it moist, and it'll rot down into a useful supply of well-drained, rich, loamy soil.

If you have some suitable garden space with fairly soft soil you've been using for growing, use that. If all you have is some rough, hard ground, don't despair, it'll do, with a bit more trouble. Put some pegs in the ground and use string to mark where the beds will be (include a 15" path space round the beds), and then cover it with a thick layer of hay, grass clippings, dead leaves, anything that'll make a good mulch. Make it at least six inches thick; if it sinks, add more. Keep it well-watered, and don't let anyone walk on it. After a few weeks the ground will be much softer. Scoop off the mulch (you can use it later, in the garden or in the compost), and you can begin.

If you don't have mulch, use an old carpet, or lots of newspapers or cardboard cartons, or even garbage bags. Give the surface a good sprinkling first (not enough to puddle or muddy it). Keep checking to see the soil is moist, sprinkle again if not.

This is another way of preparing lawn for growing beds rather than removing the turf, though it'll take a while. Carpets work well.