A cover crop, as mentioned earlier, is probably a solid place to start. Making the transition from conventional can take a bit of time, and growing a grass/brassica/legume mix can be a good way to ease into the transition. Any organic matter that can be applied will help, apply and then plant.
Grazing your cover crop, and whatever weeds sprout, is an excellent way to help the transition process (as long as the nitrate levels in the soil are acceptable). Grazing will additionally add a nice manure/urine spread.
Cattle are essentially fermentation tanks on 4 legs, and can be utilized as a wonderful tool to achieve your goals (sheep and goats will too...I prefer working with sheep in small areas and cattle on larger ground, but goats are awesome as well). A ruminant passes 85% of the nutrition through it's gut, photosynthesis can make up the rest along with healthy soil life. If you really want to get into it....run poultry too, as they help to balance the nutrient content. Geese are good grazers too, and can be used in small areas if you don't want to mess with larger stock.
If you have livestock, put them into a paddock (size depends on your land and desired stocking rate) and
feed them
hay while they graze. It will provide the livestock extra nutrition, and any waste will not be wasted but rather turned into fertility and water holding capacity. This is a great way to avoid hauling manure/compost as well.