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I have been making my living growing produce organically for the past 14 years. For 8 years i was certified organic. I assume you don't care to get certified, you just want to grow pure food.
http://www.idigmygarden.com/forums/ is a great forum to learn the ropes. Organic gardening also has a really good forum and the magazine is an excellent resource http://www.organicgardening.com

It will take many years to get you soil in shape and learn the techniques for successful organic growing so don't expect a great garden for a few years. Start small, no more than a 10' x 10' (3m x 3m) garden the first year or you will get overwhelmed in august when the weather is hot, the insects are out and the weeds are growing high.

Mulch everything with straw (not hay as hay tends to have a lot of weed seeds) and mulch well-at least 6" thick. Straw mulch will keep weeds down, moisture in the soil and blight from happening on plants like tomatoes. It also adds organic matter to your soil.

Have a good hoe, rake, wheelbarrow, trowel and garden fork as your basic garden tools.

Start a compost pile ASAP, compost will be the main thing you will feed to the soil/plants. Compost is the best thing to build healthy soil and organics is all about building healthy soil as any organic grower worth their salt knows soil is alive and healthy soils means healthy pest free plants.

Good luck

it would be the same as any other garden except you won't be using any chemicals.

You are asking a huge question. There are big books written about this subject. Since you ask a broad question I will answer it broadly.

Growing plants organically is a lot more than avoiding chemicals. It really is about healthy soil.

http://www.rodaleinst.org is one of the most complete sites devoted to organic growing

But start with the soil. Fertilize with compost, green manures, natural mulches. Start a compost pile ASAP

Have a crop rotation plan (this is important for even the smallest gardens)

Find certified organic seed to plant

Control insects through a variety of methods including crop rotation, exclusion, hand picking, beneficial insects, selective spraying (most organic pesticides, and yes they do indeed exists, are broad spectrum so you want to use them sparingly so you do not kill off the beneficial and neutral bugs that make up 97% of the bug population), trap cropping etc..

Hoeing and mowing to control weeds

I use chicken manure and cow manure from our farm. I put it on the ground and till the dirt about 10 times before I plant.
I don't use anything to debug or to control weeds. If I see bugs, I pull them off. Once my plants are big enough, I let the chickens control the bugs. I also weed the garden about three times a week.

I highly recommend using fish /seaweed mix…I uses Neptune's Harvest. Buy it in concentrate form..mix teaspoon per gallon. Works great for vegetables, squash and pumpkins. I got it at local nursery.

Square Foot Gardening.

http://www.squarefootgardening.com/

That depends on the vegetable and the method of storage.

The Muse

It depends on the produce. Green peppers are not ripe peppers so the seeds will be immature. to get pepper seeds you need to use a ripe (red, yellow or orange) pepper

tomatoes you can use the seeds but you need to ferment the seed first than dry them which takes about 2 to 3 weeks to do properly so you don't get seed born diseases.

Dried beans will work. Potatoes will work but get only organic as the non organic kind have a sprout inhibitor and tend to have more diseases (seed potatoes are certified disease free)

Strawberries and raspberries do not come from seed but from plant divisions and runners

leafy greens are harvested before they go to seed.

Melon seed would be viable but these are almost always hybrid AND they are not grown in isolation so the seed would not only be hybrid but would have crossed with any other melon varieties grown within 2 miles so what ever grew would be nothing like the melon you got the seeds from. This would be true of zucchini, cucumbers and all winter squash as well.

So in theory you could grow a garden this way but few if any of the crops would come back true because most everything is hybridized and since none of these crops were grown for saving seed you would have a lot of crosses on top of the hybrid crossing.

If you want to experiment go for it, if you want a garden from which you can eat the food (by this I do not mean any food you harvest will be inedible, it won't. I am saying you probably won't get a lot to harvest) buy seed.

Study up on what plants ward off pests. Like onions and marigolds. Then be prepared to plant those along with your tomatoes and cucumbers and pumpkins, and maybe your watermelon too. Go to the library and look up some information. Your local gardening club organization could probably help too.

Contact your county extension agency and ask if there are any gardening classes.

Some websites
http://www.rodaleinstitute.org
http://www.gardenweb.com/forums/organic
http://forums.farm-garden.com/index.php
http://alanbishop.proboards60.com/index.cgi
http://www.johnnysseeds.com

Pepper plants are good for unwanted insects.

You can also use dish soap. Nothing fancy just regular "Joy" soap cheap soap only. But, there is a good chance you will kill the good insects too.

1st: Get a bucket, fill it with water

2and: Pour the soap in (not to much because you don't want to get rid of all the good insects)

3rd: stir it up so it can blend. (not to much suds)

4th: Let the bucket of soap sit out in the sun for at least a couple of hours.

5th: Use a sprayer and distribute it all over your plants.

See the soap gets in the insects esophagus and the insect dies because it can't breath.
You can use this anywhere in your yard.
works GREAT for cinch bugs.

To get a good organic garden going takes years of soil building. start small as a big garden will get overwhelming come the hot part of summer. I would say a garden no bigger than 10 feet by 20 feet the first growing season.

Now is the time to start garden prep by choosing where you want the garden and opening up the sod. smothering the area where you will have the garden is a good first step or you can plow the sod open and till it in next spring. plowing is a lot more effective than tilling for killing grass.

You will also need some tools. Get a couple of hoes, my favourite is the shuffle or stirrup hoe. You can find these at any box store. they are lighter and easier to use than the standard concrete hoe most people think of when they think about hoes. You will also need a wheel barrow or garden cart, a potato fork (looks somewhat like a pitch fork but fatter), a shovel, a spade, a couple of trowels.

You will need seeds. My favourite place to get seeds is Johnny's Selected Seeds in Maine. http://johnnysseeds.com
Start with easy things to grow and pay attention to the fact not everything grows in every season. Lettuce for example is best planted in the spring, it likes cool damp conditions. Tomatoes and peppers like it hot. A good seed catalogue will tell you such information. You will likely want to use seedlings for a lot of things such as tomatoes. Do not buy these at places like Wal-Mart. Go to a local nursery and tell them you are just starting out and you will get a lot of advice. One caveat, most nurseries (and box stores) are NOT organic and do not know much about organic growing so ignore all advice to use chemicals. But you will find healthier seedlings at most local places than box stores.

Good luck

First of all, way to go in trying organic!!. Ok now I would try to get rid of the granite rocks because they dont really serve a purpose. As for removing the the top twelve inches then bringing in newer topsoil, I wouldn't do it. You'll waste money. The soil that the city put in probably is light brown because yes it is sorta dead. But you got it right with the humus. Also well rotted and composted manure will help also. A cubic yards worth of organic material would do wonders to about 50 square feet of area. Look for these materials at the garden center or if you can look for yards that sell bulk material.