Every year around March a Call for Admission is issued, stating the number of available positions and fellowships (including grants from external research institutes, e.g. INFN, INAF, etc). Some of the fellowships may be reserved to foreign candidates.
The selection process (which takes place about a month after the deadline) includes the evaluation of the candidates’ cv and of a research project, and an interview which can also take place remotely (i.e. using Skype).
Updated info can be found (IT) (EN)