Quick and Simple Instructions:

Edit a page and add a Search Core Results web part.

Edit that web part and expand "Fixed Keyword Query".

Add the fixed keyword query (e.g. ContentType:"Training invoice" TrainingInvoiceNumber:1111)

Expand Results Query Options and change "Cross-Web Part query ID" to a value other than "User Query" (e.g. "Query 2").

Notes:

Using core search results in this manner allowed me to create a page that shows information from another site collection.  The client has two major site collections: Departments and Products.

The product site collection contains, naturally enough, product information.  Each product in the site collection aggregates data from multiple sources.

One of the departments, codes and testing, is on such source.  When users access product XYZ, they should see codes and testing data directly on the XYZ main page.  Since codes and testing is hosted in another site collection, it's a little awkward.  We decided to use the core search results web part since search spans site collections.  Codes and Testing manages product data via a custom list that is constrained by a specific content type.  Aa keyword query that uses first the content type and then the product number narrow down the search to a single row in the custom list.

The keyword query above is an AND.  It returns documents of content type "Training Invoice" and where the invoice number equals "1111".

A nice benefit from this approach: We can edit the XSL from the core search results web part and generate any format that we want. 

See here (http://devcow.com/blogs/jdattis/archive/2007/04/17/SharePoint_2007_How_to_Rollup_Content_from_multiple_Site_Collections.aspx) for another blogger's discussion on this topic.

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