There's a few products around to aerate the lawn as already mentioned. One of the quirkiest is the spiked sandal that is fixed to the bottom of your shoe. As you walk over the lawn, they penetrate to a depth of about 3".
The draw backs are that you will rapidly find yourself walking like a fully paid up member of the department of funny walks (Monty python) as you try to get maximum penetration and at the same time avoiding stabbing yourself in the calf muscles. They do work (sort of) if used regularly.
The best home use product that I've ever seen is as New Shoot stated. There is a hollow tine aerator "Fork" that you go over the garden with. It takes out a core of soil leaving a hole in the lawn. You SHOULD brush sand into the holes to stop them closing up and to improve drainage. You might also look to hire a small aerator. I've not seen too many around lately which are small enough to get into the average back garden. There used to be one made by a company called Sissis. They are a company specialising in the manufacture of specialist ground care products, and used to make a motorised machine with a 20" wide, spring loaded, spiked drum that you "drove over the lawn"
Sadly I've not seen one of these recently. I expect that 'elf and safety has killed them off (first hand experience tells me how easy it was to injure yourself with it)
There are several "slitter" type of machines around and about, they tend to do the same type of job as scarifying, ripping out Moss and Thatch. The idea is that they also cut the roots of the Grass which, if carried out at the right time of year, will also encourage fresh root growth.