Communication is crucial to the success of group work. Therefore, define from the start the means of communication that will be used in the group (email, discussion groups, meetings, etc.) and use them in accordance with the common rules that you will have set.
Another key point is organization. To be effective, follow these steps:
set common objectives that are understood and agreed upon by everyone
discuss the distribution of roles and tasks; you can use this document as a guide
plan all the steps of the work, without forgetting to plan individual and joint proofreading of your productions; a good use of the commenting and editing features available in most writing tools will be of great help for this stage.
Many software exist to facilitate collaborative work, some of which are free and open source. Depending on your needs (type of document to produce, synchronous (= simultaneous) or asynchronous work, etc.), select the one or ones that suit you best and make sure that each member of the group has access to them and knows how to use them.