As far as I know, there is no offical apps of Blogger.com on Android. I found some apps required to sign up some other parties accounts. They cannot give you a direct access to Blogger.com. But I found AndroBlogger, that is a free apps. Moreover, it can access the blogger via your Google account. I think it uses the blogger API.

The apps is fairly simple. You go to "Settings" and you fill your Google account details.
Then you can write your post in "Create new post".

But it only works very well when you has a single blog. If you have more than one blog under a single google account, it can write the last updated blog. Moreover, that is text only environment, you can post photo from your phone. In my situation, that is already good enough, I just want to write a quick post while I am having lunch or waiting a bus.