You need to get the basics clear. You don't make sites ON Google. Google just searches through it's database of web pages of the internet to look for results queried by the user. So when you create a new site, i.e., a domain, through a domain registrar, search engines like google/yahoo have a bot (called spider) to crawl your website which then gets included in it's database.
Although, yes, you can create domains through google (it probably uses a third party service for this). Here you go, *www.google.com/a/cpanel/domain/new. It includes Google Apps services. You can select either of the two options, business/personal, depending on your preferences.
Also, you may want to keep an eye for the server you will be using to host this domain. It will hugely affect Google Apps services.