My name is XXXXX XXXXX you for your question.
To be brief, lawn aeration of Bermuda grass is best done in the late spring, early summer when rate of growth of the grass is very very fast.
Some people do this later in the year say during the fall, but at this point if grass growth has slowed it may mean weeds can take over. The best time again is late spring, early summer when the soil is still moist, the grass is growing rapidly. Too early and you risk some damage to the partially dormant roots. The weeds and clovers usually are overtaken by the Bermuda once it gets into its prime growth.
The easiest way to do this is to rent an aerator from home depot or your local home improvement store, each of them should have lawn aerators for rent.
Tip: PLAN IN ADVANCE. Everyone who doesn't own an aerator will want to rent so keep in mind there may be limited supply.
Basically there are spike and plug aerators, depending on the type of soil you have a plug aerator is best because of the removal ,where a spike just STICKS a hole, a plug pulls a small amount of soil up and creates these channels for root growth, air and water to help it recover.
Easiest way to aerate is to mow the day prior then water the lawn very well if you can, or perhaps plan on doing it if you spot rain in the forecast. Then ideally you would aerate starting the following morning the when the grass is moist and cool(ish) not scalding hot at high noon.
So after the prep the day before, you basically just run it over your entire lawn to get full coverage in 1 direction, then do another full pass over the lawn but this time do it 90 degrees to the direction of the first pass. We do this to ensure full coverage and adequate aeration. In other words cover the whole lawn lengthwise, and then go back and cover it widthwise.
If you like you can fertilize lightly, however not everyone does this. Some believe it helps the recover of the lawn from the aeration.http://www.homedepot.com/StoreFinder/index.jsp
Use this link here to find your local home depot stores and to call to see what the schedule looks like for renting an aerator.
Doing this is a really cheap and easy way to keep a lawn looking super fresh all the time with great growth, especially if the lawn is used - it helps keep it healthy and lush.