Thoughts on Core Aeration

Our soil is clay and it compacts pretty badly. Ive read that core aertion can help with that and that it improves the health of your lawn. thoughts?
Also, to help the health of our lawn, I want to help the depth of the topsoil. However I don't want to start our lawn over and nor do I have the money to get truck loads of soil dumped. So would adding a little soil over time be a good idea? I figure the grass will grow up over the new soil and given time, the topsoil depth will improve. Thoughts?

Paul's recipe for healthy lawns for the cheap and lazy can be found here:

https://permies.com/t/11/lawn/organic-lawn-care-cheap-lazy

Enjoy! (remember that when eating an elephant you have to take a bite at a time; I'm not suggesting that you will be able to implement everything immediately but you will find information that helps with whatever method one might choose for multiple areas or an entire yard.

I read that page that you mentioned. It doesn't mention anything about aeration. At least not that I saw. Any more thoughts?

In the long run it would be best if worms could handle all of your aeration needs. If you use an aerator with a good core size it may be possible to rake some nice compost or sandy loam into the holes immediately after the machine is done. This would allow for some surface drainage and would give worms a place to start. Quite a bit of material could be added without covering the grass completely.

Great idea Dale - and if there are no worms in the lawn (there probably aren't) you can always put some there after following Dales advice. When I first started introducing worms to my sterile yard I just went into the nearby woods and dug around under the leaves a few inches under the dirt. Now eight years later I have plenty of my own -- but -- it does take a while. There are still patches that are just bit of grass over hardpacked sand - I'll get it all converted to good soil one day.