Lego has a tool named LEGO Digital Designer that allows people to design their LEGO creations virtually before they every pick up a brick. And once you have your digital design completed, it will generate build instructions for you.
FIRST LEGO League (FLL) teams around the world have published designs on a whole wide array of components to help new teams and teams struggling with a game challenge figure it out. Here are a few published designs that you can download and then open up in LEGO Digital Designer to explore. Once you have them in the LEGO Digital Designer you can change, modify or build them to get a better understanding of how they work.
Both images above are from https://rebrickable.com/mocs/MOC-10638/DLuders/super-small-box-robot-by-fll-team-moscow/
If you are looking for things to do before the team get together check out these box designs.