You can find all the links on Werner Vogel's blog. I share his enthusiasm for the new host-a-website feature. I was asking for it for a long time. I guess, from reading the tea leaves, he was too.
Anyway, I had to do a bunch of trial and error to get my first S3-hosted static site configured. I wanted to leave a howto behind me so next time I won't have to do the head-scratching again. Maybe it will help you too.
Suppose the domain you want to host on S3 is r2.reallysimple.org. And the index file for that domain will be index.html. This is what you do.
1. Go to the S3 panel on the AWS website and create a new bucket called r2.reallysimple.org in the US-Standard region.
2. Upload a file called index.html to the new bucket. Say something simple like Hello World. You can copy the HTML from my test file if you want.
3. Click on Properties at the top of the right panel, then click on Website in the lower-right panel. Click the Enabled checkbox, and enter index.html as the Index Document. Click Save.
4. Click Permissions in the lower-right panel. Then click on Edit bucket policy. Paste in the template text you grab from this file. Edit it to replace YOUR-BUCKET-NAME-GOES-HERE with the name of your bucket (in the example r2.reallysimple.org). Click Save.
5. Now go to your domain registrar, and map r2.reallysimple.org as a CNAME to r2.reallysimple.org.s3-website-us-east-1.amazonaws.com.
Now you should be able to go r2.reallysimple.org and see the text of your index file.
I just read a review of five URL shorteners and added a comment recommending the one I'm building my systems on, Adjix.
Adjix is imho, the best because it automatically stores each link it shortens in an Amazon S3 bucket that I own. If they ever go away, or if for some reason I decide to move on, my links won't break (at least not because of them). I also use a custom domain for my URLs. So I get complete data portability at no cost. Absolutely no lockin.
I don't own any stock in Adjix, or have any reason to recommend it other than it is a great service.
I know a lot of people haven't heard of it, but it's really important. Someday a lot of these links are going to break. I'm doing everything I can to be sure that mine last. I know other people care about this. Adjix has made it work.