The disclaimer is that if you're converting a lot of documents you'll be better off with a supported well-integrated solution that fully uses FrameMaker's DITA support. If you're looking to do it on the cheap though (and who isn't) you can do this conversion by using straight XSLT and framemaker templates.
First create the framemaker template to handle the appearance of the document, then use XSLT to map your DITA content to the content tags you've used in Framemaker.
You can use the free SAXON xslt interpretor to do the actual conversion.
Here is some of adobe's reference material on authoring new DITA documents:
http://help.adobe.com/en_US/FrameMaker/8.0/05h/dita.html
Info on Framemakers's native XML support is here:
http://www.adobe.com/products/framemaker/pdfs/xml_fm7.pdf
The framemaker manuals also cover the subject quite extensively. Hope that helps