Thank you Jennifer! I used key words to search related thread. I just thought that maybe there is other simple ways to save MyMap into local computer with pdf or jpg format.
I went through the "Creat PDF" thread, I tried the method, then I think what Dominique said is the most convenient way to save the map as a pdf file by using PDF printer. So right now I can use this way. But I will ask my team leader for sure.