Round-Robin Brainstorming is very straightforward:
Step 1 – Gather your team together around a table. Give each person index cards so that they can record their ideas on individual pieces of card.
Step 2 – Acting as a facilitator, explain the problem that you want to solve. Be specific about the objectives of the brainstorming session. Answer questions, but discourage discussion. The goal in this step is to allow individual people to think creatively without any influence from others.
Step 3 – Have each team member, in silence, think of one idea and write it down on an index card.
Step 4 – Once everyone has written down an idea, have each person pass their idea to the person next to them. Everyone should now be holding a new card with their neighbor's idea written down on it.
Step 5 – Have each person use their neighbor's idea as inspiration to create another idea. Then ask each person to hand in their neighbor's card, and pass their new idea to the person next to them to repeat step 4.
Step 6 – Continue this circular idea swap for as long as is necessary to gather a good amount of ideas. When the time is up, gather up all the ideas. You can now collate them, eliminate any duplicates and discuss them further as required.
A Round-Robin Brainstorming advantage is that your group uses other people's ideas to generate even more ideas, without being influenced by assertive or vocal members of the team. Another advantage of this approach is that it also ensures that everyone in your group gets an equal chance to present their ideas. If your team has shy or low-confidence members, this method can help them feel more comfortable.
A disadvantage of Round-Robin Brainstorming is that it isn't anonymous. When team members pass ideas around the room, they might hold back simply because they know the person next to them will see what they have written. Another disadvantage is that each person gets inspiration for their new idea from the ideas of only one other person, rather than from the entire group.
Tip:
You can make Round-Robin Brainstorming anonymous by gathering the ideas at each stage, shuffling them, and then passing them out again (Rather than having group members pass their ideas to the person next to them).
Instead of writing ideas down, you can also use Round-Robin Brainstorming verbally. Seat your team members at a table, and discuss the current problem. Then, go around the table and allow each member to state one idea. Write down each idea for further discussion.
This is often faster than the written variation. However, some team members may be hesitant to present ideas in front of the group. Help avoid this by letting everyone know that no idea is unworthy of discussion.
You can also use Round-Robin Brainstorming with larger groups. Divide everyone into smaller groups, and have each group develop one great idea and write it on an index card. Then, rotate cards between groups, just as you would with the individual variation. You then have each group brainstorm a new idea based on the previous group's card.
Source: http://www.mindtools.com