Mow regularly to keep grass clippings short. Leaving the clippings in place, as a mulch every third clipping not only saves the trouble of raking them but also returns nutrients to the soil.
'Shampoo' your lawn with a spray of biodegradable liquid detergent (5fl oz/150ml in 10 gallons/45.5 litres of water for every 1500sq ft/140sqm of turf) to reduce surface tension in the soil and allow fertilisers to penetrate more effectively. Apply to dry ground.
To rebuild garden soil naturally, plant a 'green manure'. Agricultural lupin, a legume that manufactures its own nitrogen fertiliser, is a good choice.
Blood, fish and bone meal are good organic fertilisers that you mix into the topsoil before planting. They act slower than chemical fertilisers but last longer.