Rake the soil with a garden rake to remove rocks and other debris. The thatching and aeration process will be impeded by hard objects in and on top of the soil.
Water the lawn or garden with a garden hose to moisten the soil. The soil should be moist enough to allow the aerator and dethatcher to penetrate the soil. If it has rained recently, you can skip this step as the soil is likely to be sufficiently moist.
Pull the thatch tool, using a series of short and vigorous pulls through the grass and soil, over the entire soil area to remove thatch. Use a hand thatch tool for smaller areas or an automatic de-thatching machine for larger areas. Guide the automatic de-thatching tool at a medium pace, allowing the teeth to adequately pull the thatch through the soil as you traverse the entirety of the lawn or garden area.
Gather the thatch removed from the lawn with the rake. Bag the collection and dispose of it or take it to a facility for use as compost.
Run a powered plug aerator over larger lawns or gardens, following a path across the entire area in a series of straight lines--like lawnmowing. Once you have finished a path going east to west, repeat the process going from north to south. The aerator will remove and leave plugs of soil 2 to 5 inches long in its wake.
Leave the plugs removed from the soil on the lawn so they can break down over time and replenish the soil with nitrogen.