Install the AAdvantage Toolbar.

When you are shopping at a participating website, the toolbar shows "Earning Miles". When you are not shopping at a participating website, it shows "Not Earning".

Often times you don't even have to link through the AA shopping portal. For example you can enter Kohls.com and a little popup says "Click here" to earn miles. After you click it shows "Earning Miles" in the toolbar.

A word of caution - some merchants require you to link through the AA portal in order to earn miles. But many do not, like Kohls.com. If you are required to link through the AA portal, the popup will let you know, you link through the portal, then you see "earning miles".

I've gotten many miles by shopping online and it's to the point I don't even worry about verifying most of the time. After several weeks the miles show up.