Toronto Islands used to be a very popular centre of recreation back in the early 20th Century, with a baseball stadium (where Babe Ruth hit his first professional home run) and an amusement park (offering a popular diving horse number!). The action stopped in the 30's when the stadium closed but it is fair to say that the Toronto Islands have regained their popularity, with over 1.2 million visitors every year.
You can only get to the Islands via the Toronto Ferry system (cash only). The ferry that reaches Centre Island brings you closest to the Centreville Amusement Park and further on to Centre Beach (with bike rental, splash pad and Franklin Children's Garden) and Gibraltar Beach (a more secluded beach to the west).
Ward's Island ferry reaches the eastern point and is the closest to Ward's Island, its beach and the residential area. The Hanlan's Point ferry services the western end of the Islands. It is the closest to Hanlan's Point Beach (with the nudist section!).
During the summer, I strongly recommend you try to catch a ferry before 11 a.m., otherwise, chances are you could wait up to 40 minutes in line with the rest of the Toronto population (it still is worth the wait!).
See my different blogs on great ways to enjoy a visit to Toronto Islands:
8 TIPS: Toronto Islands with teenagers (also good for girlfriends).