Redox reactions are fun; just remember LEO GER (loss electrons oxidation, gain electrons reduction) and that reducing agents are oxidized and oxidizing agents are reduced. Whichever element gains electrons [charge becomes less positive or more negative] is oxidized, making it the reducing agent.
Looking at the charge on Mn
Since the overall charge on the reactant-side molecule is -1 and O is always -2, Mn + (4 x -2) = -1 Mn would have to be +7
To balance the charge, Mn7+
Mn is gaining electrons; remember "GER." And if reduction is occurring, MnO4-
in this equation is the oxidizing agent.
Hopefully that helps!