To recap, go to smile.amazon.com, use your normal Amazon log-on credentials, then choose a charity from their list. It's free, and you're shopping the exact same Amazon.com as you always have; there is no difference in pricing or available products. Your existing shopping cart, wish list, wedding or baby registry, and other account settings stay unchanged.
Without you having to do anything else, for any qualifying items you buy Amazon will donate a small amount to the charity you selected. Eligible products are marked “Eligible for AmazonSmile donation” on their product detail pages. Just be sure to always go to smile.amazon.com rather than Amazon.com.
Admittedly, the amount donated is quite small: 0.5% of the purchase price from your eligible purchases, minus any rebates, shipping & handling charges, gift-wrapping fees, taxes, or service charges. But it's a crowd-funding concept. I buy $100 of stuff, and there is a 50-cent donation. Twenty thousand people buy $100 of stuff, it's a $10,000 donation. The more the merrier.
You can read the FAQs about the program here: http://smile.amazon.com/about.