If you're looking to go organic and want to avoid spraying potentially dangerous chemicals on your lawn where your children play and your dogs runs around, then you should consider using an organic fertilizer. You can't not use fertilizer, unless you want a lawn with bare spots and weak plant growth. Luckily, there are lots of natural, organic fertilizers at your disposal. Many of these have been used by farmers for years. In some cases you can get a commercial formulation that will include a variety of these natural ingredients.
This fertilizer is made by drying out the shells of shellfish and pulverizing them into a fine dust. This dust contains lots of calcium, as well as another mineral called phosphorous. You don't have to worry about the fertilizer having a fishy smell, since all of the liquid has been removed from the material before it is packaged. Another really good benefit of the shellfish powder is that it has a natural chemical in it called chitin which will drive off pests (which means that this crushed shellfish fertilizer also does double duty as a natural pesticide).
Blood meal is made by drying out the blood of cows. It's super rich in nitrogen. It is used by florists and gardeners who want to really boost a plant's flowering ability. However, blood meal is incredibly powerful, and you have to be wary about over using it or you risk burning the soil, which will ruin the plants. This is why you want to be very careful about adding blood meal to your lawn. A little is great for promoting bright green color, but use too much and you will end up with brown spots. So, it's better to get a mix that includes blood meal and not just add it straight unless you are a well seasoned gardener.
Pulverized Stone Phosphate
For people who might be ethical vegans and don't want to use cows blood or fish shells, an excellent fertilizer option is crushed up stone. It is based on either calcium or lime based rocks and is filled with minerals. One of the really cool things about using pulverized stone fertilizer is that won't leach out from your yard. Its stays in the ground until the grass needs it and sucks it up.
This is one of the most popular fertilizers because it has everything the plant needs. You won't need to mix and match different materials. However, one thing to be careful of is using fresh manure. Like blood meal, it is very rich and can burn out your yard. So, it's best to used aged manure.