Remove the Old Sod
If your lawn is really small, shovels and a mattock may do the trick. Otherwise, rent a sod-cutter to shave off the top grass evenly and a rototiller to create optimum soil.
Get rid of the old turf debris. Use shovels and garden rakes to remove what the sod-cutter can’t reach. Hopefully the old turf rolls up, but may have to come out in chunks. Use a wheelbarrow to haul it out of your way.
Do not simply till old turf in with the underlying soil. This can lead to a number of future lawn problems such as fungus growth and it makes it harder to grade the soil.