The vehicle the user is searching for can be displayed anywhere within your site, to provide a clear reference point and provide a more personalized customer experience.
The search filter can be moved from the left column to the right column, or any other section ("reference") your Magento template provides.
You can use the search block from within a Magento template, for example page/html/header.phtml to put a search in the header (this is good in "horizontal" mode).
You can include the vehicle search from within a Magento CMS page
The design guide also gives tips on designing horizontal vs vertical vehicle searches.
You can easily target specific parts of the search with your CSS to style it.
The my vehicle feature is currently implemented as an optional snippet you would copy paste into your Magento theme. Other similar snippets are available in the documentation under the "optional snippets" section. For instance you could place at the top of your category pages a message that stated "showing all products for your 2002 Honda Civic". Another example is the snippet which allows you to add a "compatabile with" list to each product details page. Be sure to check out the Optional Snippets in the documentation to see all that is possible.