How can I observe Sgr A* with itelescope.net I've been experimenting with itelescope.net and tried to observe Sgr A*. 

I was wondering if there are any suggestions how I can best observe the surrounding stars.
I expect that all the itelescope.net instruments work at visible wavelengths. Therefore you have no chance at all to image the stars around Sgr A*, since it is behind about 25-30 magnitudes of optical extinction, caused by dust between us and the Galactic centre.

The published images you have seen were taken by large telescopes working with adaptive optics in the near-infrared (wavelengths longer than 1.5 $\mu$m). At these longer wavelengths the extinction caused by dust is only 2-3 magnitudes.