1) Since you're living in down town, just head north along Du Parc, climb all your way up.
2) Green line to Guy-C O N C O R D I A, take a bus at the entrance of Guy-C O N C O R D I A metro, which goes to Cote-De-Neige (I've forgot the bus number, but you can just ask somebody there, it always has lots of people around.)
3) Orange line "Mont Royal" metro station, it's the back of the mountain