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You basically just have to share the document on which you want to collaborate. Open the document that you want to share and click on the blue rectangle on the top right of the screen. You can enter the email addresses or names of people that are in your Google “circles” that you want to share with. The editor, aka you, has control over what they can do. There are some videos on YouTube if you want to spend about 5 minutes watching them. Really, that’s overkill, it’s easy to do, but since you have a group with presumably different levels of familiarity with Docs, perhaps it would be a good idea if everyone watched the training video.
Here is a good, concise youtube video on collaborating with Drive: http://youtu.be/Dsoa9skxVuk