To start, brainstorm for ideas. Let your imagination go wild, throw all ideas, even the craziest ones. If you have really no inspiration, look at past projects, but be careful to use them; to be original and not to repeat other teams' projects. Try to think of what annoys you in your everyday life, what problems you would like to solve, what you would enjoy working on. You can go through the hot topics in scientific journals and news articles. And then, think about possible applications of the synthetic biology techniques that you have learned and other interesting technologies that you know.
There may be different types of projects. Some are foundational, for example MIT iGEM team introduced a BioBrick standard or the Slovenia iGEM team in 2010 created a DNA scaffold for enzymes.
Another type of project can be an applied one where you use an engineered organism to perform a specific task like cleaning water from a pollutant, biosensoring or producing a protein.
Other projects can include the use of a specific technology, bioart or a business-leading idea. However, most of the High School projects fit in the first two categories.
To do a brainstorm, first try to come up with a list of ideas individually. Then organize a meeting or even an entire weekend where you discuss your ideas with the group.
When you brainstorm, you should think about some simple rules in order to be successful. When brainstorming, quantity IS quality. The more ideas you throw, the higher chance you will find a valuable one. You need to feel comfortable in your group. Don't be concerned that other people will judge your idea. Be aware that constructive criticism is good. During brainstorming sessions, try to just add more new ideas. The originality and uniqueness of ideas is very important, so unusual projects are even more welcome. Then, after creating a long list of ideas, try to group them by topics, make a mind map, modify and combine them.
In our iGEM team Paris Bettencourt we played one game that we found very useful in brainstorming. We divided the team into groups of 2-3 people, we brainstormed and then every group picked an idea that another group created. Then, they added something and pa**ed it to another group. In this way, everyone adds a little piece to the idea and everyone participates.
At the end of the brainstorming session, the group should be able to make a list of final projects with graphics and schemes. Spend some time to learn more about your ideas, read articles and ask your teachers and scientists from the field. One of the most important parts of the brainstorming is to select at the end the ideas that are useful.
First have fun exploring all things that you could do, and only later take into account some limiting factors such as your budget, equipment or expertise in the technology that you're aiming to use.