To use Google Docs within Blackboard, create a Google Doc and then post a link to it in your Blackboard course. You may also choose to embed a copy of the document as a preview for students.
The first time each student clicks the link to edit the document, the owner of the Google Doc will receive an email requesting access. You may click the link in the email to grant the student access to edit.
Here is a video demonstrating the process. This video has audio.
(direct link to video http://screencast.com/t/N7ZHgTELbk)