Amazon S3 & domain name question: How do you use your own domain with S3?

Hi everyone,
I am new to the webdeveloper community and am trying to set up a website by myself. Although I have some experience with maintaining websites and editing, uploading, etc. of a website via an FTP client like WinSCP and SSH Tectia Client, I don't know much about how to actually launch one's own website and getting it hosted somewhere, etc.

I did some research and saw that I could purchase a domain name for a year through Google via their partner eNom for $10 a year. Then, I did some more searching and saw that Amazon has services, such as the S3, for which I signed up. My issue is, I bought the domain name that I wanted and would like to be able to use it instead of having my site that I am trying to build have a very long "amazonish" link to it. I don't mind if the images and things like that are housed under those long URLs, but is there a way to have my "index.html" page (the homepage) and other site pages be under my own ".com" domain?

For example:

I bought the domain: (I didn't actually buy "mysite.com", just using it as an example! )

Can I use <www.mysite.com> with Amazon S3, and have "www.mysite.com/index.html" and all other pages to have a "www.mysite.com" prefix URL instead of very long "amazonish" URL?

How does a site like www.theoatmeal.com have their own site and pages, etc., but their images are under the Amazon S3 umbrella, for instance: http://s3.amazonaws.com/theoatmeal-img/thumbnails/bobcats_tuesday_big.png

Or is this site hosted at two different locations or something? I don't understand this .
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Any help will be much appreciated!

Thanks!