Aerate your lawn in the Autumn every two to three years after you have scarified. Aerating means 'introduce air into'. By perforating the soil with your garden fork, you are letting carbon dioxide and oxygen circulate, and water and nutrients down into the lawn root zone.
Push the fork in about 4-5 inches deep and pull back a little, repeating every 6 inches across the garden. You can leave the holes as they are or, especially if you are working to improve the soil, you can sweep in an appropriate mix of sand for drainage, compost for fertility, and/or leaf mould for water retention.
Planting spring-flowering bulbs at the same time as aerating your lawn is a two for one job.
Once you're scarified your lawn, which can be done in spring or autumn. You can aerate your lawn at the same time. The reason you aerate your lawn is to introduce air and nutrients back into the soil and to break up any pan` or any compaction in the soil. After you have aerated your lawn, you can brush a mix of sand and compost into the holes, or you can just leave the holes as they are.
For small lawns, a normal garden fork will be all right to aerate your lawn. Just push it in between four or five inches deep and pull back, so the grass lifts a little. Pull it back out, move back about six inches, and then do exactly the same again. If you've got a very large lawn, you can hire an aerator, a mechanical one, which will do the job. Just a normal garden fork, that's all you need, just straight in the ground, kind of lift it up.