It may not be absolutely correct that we garden organically. Why not? We use some elements of our fertilizer that don't come from certified organic sources, for example, seed meal (such as cottonseed, rapeseed, etc.) and bone meal. I don't know of sources for these items that come from certified organic plants or processes.
Our nitrogen, phosphate and potassium come from natural, though not necessarily organic sources. But there are no chemical sources that depend on fossil fuels.
Furthermore, we compost just about everything that is safe to compost, including our kitchen scraps, plant and weed trimmings (with exceptions for poorly behaved weeds), and occasionally we include some horse or chicken manure in the compost. However, we do not apply fresh or partly composted manure directly to our gardens, we ensure that everything is completely cured (at least six months) before it can go to a garden. Each year we use up our supply of cured compost, so it would be nice to have an external source, but most commercial compost starts with "forest products" which means wood, which takes a long time to decompose (and it obviously hasn't had enough time in the supplies I have seen).
For the 2014 season I experimented with spraying a solution of water and fish fertilizer on my tomatoes. This foliar spray appears to have been effective in providing necessary trace elements that the very clayey soil wasn't. The tomatoes were looking puny and pale until I began this regimen every ten days or so.
As you can tell from the section about weeds in this wiki, we attack weeds directly and with a vengeance.
The only "insecticide" that we apply is Neem oil, a natural product of an African plant. I'm not sure whether Neem is an insecticide or a repellant. I read that a bug must ingest a bit of a leaf that has been treated with Neem oil (a 0.5% solution), and I don't know if it kills the bug or whether it just decides the eating isn't good there.
Whichever, I find Neem oil is not very effective in keeping pests, especially cucumber beetles, from chewing up bean leaves. It's the seedlings that most need protection and there isn't much Neem oil that sticks to the little leaves. Wait till next year!