Establish a leader. Whenever things are done in a group, it is important there is somebody who will keep the group organized. The leader should be disciplined, organized and a good motivator.
Decide as a group what you want your research paper to sound like. Your paper needs to have a voice established before you start writing, otherwise you risk getting lost in the process of writing it.
Divide roles. If possible, let every group member write about the area she is interested in the most. The whole group should write the introduction, conclusion and transitions between sections, so the text will flow naturally.
Keep things in check. Once the work has been distributed, group members should get to work. The leader should check in with them about a week after to see how everything is coming along, and address possible problems or new issues that were stumbled upon during research, and which might take the paper in a different direction.
Revise before the deadline. Each section of the research paper should support the point you were trying to get across with it. This is very important in group writing, as people tend to see things differently, no matter how much discussion and direction they were given beforehand.