Operating your greenhouse using organic gardening methods is similar to doing so using chemical methods. The main difference is that you will need to substitute organic soil augmenters and fertilizers for chemical. Provide each type of plant with specific soil additives and fertilizers appropriate for the plant's growth stage.
Make or buy compost. Compostable materials include farm animal manure, straw, pesticide free crop residues or fruit and vegetable waste, grass clippings, sawdust or wood waste, newspaper, and leaves. Consider adding plants culled in the process of selecting strong, healthy plants to your compost pile. As long as your culled plants go into a frequently turned compost pile or composting system, you should have no problems with weeds.
Mix your compost with soil and other soil augmenters. Although you can grow directly in compost, most seeds, seedlings, and plants do better with soil mixes optimized for the type and age of the plant. Soil augmentation can include sand, sphagnum moss, perlite, vermiculite or coir fiber.
Add organic fertilizers as needed. Although compost offers good soil nutrition, some plants do better with additional fertilization. Common greenhouse organic fertilizers include meals, like alfalfa, blood, cottonseed, and fish meal. Dried manure and bat guano are commonly used to augment greenhouse soils as are things like rock phosphate, wood ash, and worm casings. If you need organic, water soluble fertilizers, use fish or kelp emulsion.