Hi Sarah,
First off you want to start improving your strength. The 'draw' as its called in girls lacrosse requires a specific skill set which is enhanced through increasing wrist and leg strength. You can strength your wrist through curls or through dynamic movements such as single hand stick rotation, like a propeller on a plane. Leg strength needs to be explosive, very similar to basketball players during rebounds or defense. Static standing into a jump or onto an elevated platform. Lunges can also help.
As far as techniques, your preferred stance and stick grip is next followed by subtle movements of your body and stick to direct the ball toward your teams strong side. All of these issues will be addressed with your private coach. Good luck!
