There are three options for personalizing your wordpress blog.
If your blog is free hosted by wordpress.com you can choose to use one of the themes made available at wordpress.com through your admin section, many of which allow for a customized header -> Dashboard -> Appearance -> Themes>
Alternatively, you can choose to undertake css customizing a wordpress.com theme or making one of your own.
Or, you can choose move to self hosting by downloading and altering a free wordpress.org template to suit.
If your blog is free hosted by wordpress.com, you can edit your theme’s style sheet or create one of your own to personalize the appearance of your blog, only if you purchase an upgrade and undertake css customization yourself. (For more detailed information see CSS Customization Upgrade below. )
If you don’t purchase the upgrade, you can choose a theme from the admin area of your blog -> Dashboard -> Appearance -> Many themes provide for a customized a header and, sidebar widgets allow for posting of unique images, etc. to personalize your blog.
Although some themes at wordpress.org and wordpress.com may appear to be the same they are not; the software is different. The sticky post at the head of the wp support forum outlines the differences between blogs hosted by wordpress at wordpress.com and self-hosted wordpress.org software.
CSS Customization Upgrade
The 15$ you pay to purchase a CSS upgrade for a wordpress.com blog enables you to to alter the appearance of your theme and but you cannot edit the underlying php code in the template. Purchasing the upgrade entitles you to customize css on one blog for one year.
The upgrade is not recommended to bloggers who do not have css customization experience. Although there is a forum and other bloggers may volunteer to help you if needs be, there is no staff support provided for learning css customization. If you are learning CSS here are helpful links.
CSS customization can be used to improve on any existing theme; you can define your own classes for use in posts; you can select the Sandbox theme and build on one of the Minimalist layouts or, opt for no stylesheet and do it all yourself.
Related posts found in this blog:
Changing your blog? start with the colors
Blog Design: Which colors do you use and why
Why having a well designed blog is important
Swing into Summer: New Themes and Headers