SharePoint 2010 uses security trimming to determine what results a user can see when searching. Unless the user performing the search has read access to the item, they will not be able to see it in search results.
On a public-facing site, you probably have anonymous access turned on already (so that visitors can get to your front page). If the forms should be available to the public, then you will need to specifically grant anonymous access to the library or libraries housing those files. Otherwise, if customers already have a login for other purposes, it's just a matter of adding their existing account access to the files (preferably via a SharePoint permission group).
Aside from permission, you'll also need to make your custom fields (Year, Type) available as searchable meta-data. This can be done in Central Administration for the server farm. Here's a Google search to get you started:
The actual name of the file is searchable by default, along with Author, File Type, Created date, Modified Date, etc.