I had the same problems with my dmc tz35 camera, 2 months after I had bought it.
First I tried to open the camera but stopped as the description I had did not match to my camera. Finally I took the vacuüm cleaner and put it on the lens especially at the interfaces of the zoomlens. in the technology age it is the easiest way and for me succesfull way to remove the dust from my lens.
My advice is therefor use the vacuumcleaner first before you start to dismantle the camera.