The search page required is a single page form with multiple free-form and drop down search selections. How to go about creating custom search page in SharePoint 2010?
Build a custom web part in Visual Studio that performs a search, you can have as many controls as you want. This would require an understanding of building custom web parts, which can't be imparted in a forum such as this.
If you have a programming background in VB.NET or C#, you should be able to pick up the differences. You can google "Building Custom Web Parts in SharePoint 2010", here is a fairly decent one I found: