How are electronic configurations determined experimentally?
There are lots of techniques you could use. Most useful would be X-ray absorption techniques such as XANES or EXAFS. X-ray emission techniques such as XPF or EDS. You could look at electron emission spectroscopies (ESCA) such as XPS or UPS or Auger techniques and EELS spectroscopy, ELNES and EXELFS. 

The important point to remember is that a small perturbation to the chemical environment e.g. by a change in oxidation state or coordination number, etc. will change the signals observed, this can lead to much more than electron configurations. 

Each has its own benefit and speciality, depending on the sample and the exact thing you are looking for but that should get you going :)