You must change your permalink settings otherwise the search form won't work. Navigate to "Settings -> permalinks" and change the value from "Default" to any other value.
Search Results Page
The search form requires a search results page to be created. Create a page and assign the "Search Results" page template, once you've created the page you need to change the option in "Theme Options -> Search Setup -> Search Results Page" to reflect those changes.
Price Filter & Mileage Filter
The search form comes with 2 ranges filter that allows users to specify the ranges within which they want to perform the search. You can configure that range here in Theme Options -> Search Setup
All of the select dropdown fields into the search form, grabs the content from your database. To add content to those fields navigate to "Vehicles" and select any taxonomy (type, fuel type, color, status, etc..) to start adding content.