Create a category of “Brands”
Goto Catalog --> Manage Categories and create a new category with Display mode: "static block only"
Add the following code to the "description" field
Create a static block
Goto CMS --> Static Blocks --> Add New Block and create a new static block with the ID like "wp_custom_menu_310", where "310" is the category ID of the brand category. Add the following code to the "Content" field:
Change images
Images can be found here: /YourMagentoDir/media/template/brand/
Change links
Simple way
Specify the brand name to search for, and copy the link on the search result in the browser. It will be something like "/catalogsearch/result/?q=Addidas"
Right way
You can use Better Store Search: betterstoresearch.com/