Where it actually matters
Sterility in the greenhouse sounds somber but in a few instances, it truly matters and saves gardeners from hassle and disappointment. Here is where I heed caution.
Starting seeds, either in small pots for pricking out or in cell packs, I use sterilized soil. The smaller the seed, cutting, or seedling, the more desperately it needs the safe beginnings. For seeds, my preference is a ten-litre bag of "Seed Starter Mix" for about $7.50. For cuttings, I use the seed starter mix, or sterile potting mix (often labelled "soilless"), blended with an equal amount of perlite. Cuttings need drainage. Transplanting seedlings into cell packs, I use a sterilized potting mix with 15% perlite folded in. Once the seedlings look sturdy, I use any good quality potting soil (which usually isn't sterile but more nutritious) and add in my own compost.
If you're thinking large scale, you can sterilize soil yourself. To sterilize the greenhouse soil for seeds, dig up some soil and let it dry till barely moist. Pull out any obvious clay. If it's heavy, mix in 15% perlite or vermiculite to improve the drainage. Those minuscule roots will want to extend easily, not flight with heavy soil. Put the soil in big flat pans with sides (recyclable aluminum roasting pans work well) to about 3" deep, and cover tightly with aluminum foil. Insert a thermometer through the foil, into the soil. Cook at 190 degrees for about 30 - 40 minutes, ensuring the temperature gets to about 180 (but not above 200 degrees). Remove it from the oven and let it cool fully, keeping it tightly covered until you use it. Unfortunately, the baking stinks up the kitchen.
The other sterility attack I make is with cell packs and pots. If they are new, use warm water and a bit of dish soap. If you are re-using last year's, scrub them well with soapy water, then soak them in a solution of 9 parts water to 1 part household bleach for 30 minutes. After soaking, wash the pots or cell packs well and you are good to go.
I use tap water for the early watering to ensure that water is clean and occasionally use a diluted copper fungicide to avoid the dreaded damp-off problem with seedlings.
If you want to make sterile soil yourself, use 25 cups of peat moss, 12 cups of perlite, 12 cups of vermiculite, 4 tablespoons of dolomite lime, and 4 tablespoons of slow-release fertilizer with the ratio of 19-6-12, 11-5-11 is okay too. Grind a litre of this mixture in a blender (truthfully), if you want it for sowing seeds. Unless you are making huge amounts, this is expensive but it is sterile and terrific for a wide range of uses.
You can work at sterilizing in other ways but the soil and the pots in your Greenhouse Garden are the ones that will eliminate the majority of threats to your plants health, and your mood