Place her turrets in choke points where people need to come through above doorways ect... then basically help support your team. Shoot out orbs or beam people if they get close enough. Don't run out into the front lines with her.
Also prepare for your turrets to get destroyed frequently. This is fine though since you can rapidly place 3 at a time. Your real ultimate goal is to get your teleporter up as soon as possible to aid your team.
Also, DON'T PLACE IT IN AN OBVIOUS PLACE. I see far too many symmetra's placing teleporters in the worst places out in the open for them to easily get destroyed.
She is best played on Defense although if you can make it work on offense for you the Teleporter can be an absolute life saver on Offense to keep the presure of a push up.
Don't listen to Demos.
Place your teleporter somewhere that I can find it easily