How do I report this to the IRS, and how do I find out all of this for myself?

IGive.com recommends that you consult with a qualified tax adviser in your state to confirm that your purchases are eligible as a tax-deductible contribution.  You can bring them a copy of your "Shopping Activity Report" as an itemized list of your purchases and the cause(s) they benefitted.
 
To find this report:
 
Click on "Stats" to visit Stats 

Then click on Tax Deduction Report for a breakdown of your donations for the calendar year. 
Click on "Shopping Activity Report". 
 
Just print this out for your records whenever you want to - the IRS currently doesn't require anything more than a listing for a donation under $250 to any one cause.