Blogging platform using Drupal 7
If I understand correctly, you're looking at either the core blog module (which isn't that great), or a combination of content types and Views.

Start here for blog building information!

With regards to the second part, are you looking to have the user create a site, and then start blogging on it?  Wordpress.org style?  For that you'll firstly need to get a solid theme in place, as well as a working blog.  Secondly, look into Aegir which is a REALLY solid, powerful tool for creating Drupal sites off the back of another site (using a site as an installation profile almost...but not quite).

There are a couple of installation/demonstration videos here and here.