Easiest approach to redesigning a WP installation is to start with Kubrick (default theme), and start messing with the CSS file. You can drastically change layout and design without ever having touched a single PHP file.
Next step is to start learning how templates work, and creating new templates by altering the PHP of these files to generate the HTML you want.
Those first two steps alone will allow to completely customize the look of your WP installation.
Further customizations affecting default behavior will require more effort -- finding or writing plugins, etc. The Exec PHP plugin is very useful though, because you can use it to customize sidebar widgets and page behavior without editing files.
I am a beginner in PHP (but proficient in HTML/CSS) and have been able to do just about anything I want to a WP installation.... it is extremely customizable, which is one of the best aspects of WordPress.