The form needs to have an enctype of multipart/form-data. You can either add the attribute directly to your form, or you can add a 'files' => true if you are using the FORM helper.
Once you have your form setup correctly, the Request item will have access to it. Assuming you name your form upload file "profile_image"...you could do the following...
public function processForm(Request $request)
{
if( $request->hasFile('profile_image') ) {
$file = $request->file('profile_image');
// Now you have your file in a variable that you can do things with
}
}
If you want to see how to move to the file and do other things with it just take a look at this... http://laravel.com/docs/5.0/requests#files