To reach Kronstadt possible only through the city of St. Petersburg as rule.
Under the Soviet regime (and even till 1996) and the city of Kronstadt and all the Kotlin island were restricted area and you could to get there either with passes from the Big House at Liteiny prospect where KGB was, or with a very few excursions.
Today everything has become mundane and boring, because common and banal urban buses (№101) connects Petersburg with Kronstadt by the northern part of the dam to from the subway stations 'Staraya Derevnya'. Also, you can use 'Meteor' speed ships from the piers on Vasilyevsky Island near to Tuchkov bridge that much more expensive and faster (40 minutes if you're lucky), but more fun and less mundane. Its look like there was/is the steam-powered icebreaker from Oranienbaum to Kronstadt.