I am looking for some introductory reference concerning Automorphisms (of finite order) on K3 surfaces. Any suggestion?

You may consult Kondō, Shigeyuki Quadratic forms and K3. Enriques surfaces [translation of Sûgaku 42 (1990), no. 4, 346–360; MR1083944 (92b:14018)]. Sugaku Expositions. Sugaku Expositions 6 (1993), no. 1, 53–72. 


You can start with Hans Sterk The aim of this paper is to prove the following theorem:
If this does not give you enough, look at the references that seem promising and especially at the papers that refer to this one. Very likely anything newer that's relevant will refer to this. Also look at the many papers of Nikulin on K3's. He has made lots of computations in the K3 lattice about automorphisms. I believe Oguiso also has a paper where he studies finite automorphisms of CalabiYau's, but this is only a vague memory, so I could be off. Someone might correct me on this.... 

