While working on my thesis, and for about a month, I did some simulation studies on another university with the supervision of another professor. I want to mention this at the begining of the section where the results of this study are reported. How do I properly acknowledge this?
A simple statement such as "This study was carried out at X University under the supervision of Professor A" would probably suffice, but check with your supervisor in case there are any local regulations that you have to follow.
For example, my university requires every PhD thesis to have a "declaration" statement after the abstract, in which you list things like funding sources, collaborators and any publications resulting from your research. Your university may require something similar, in which case you would put this statement there.
Apart from the mention, you'll also need to mention this as a part of your affiliations. You can also check what both universities' guidelines say about how to mention your affiliations.