Walk down to the Quay--and catch a ferry or a hydrofoil. Ferry takes about 3/4 hour; hydrofoil about 1/2 hour. The other way is to catch a bus but it's now where near as pretty and will take much longer. Don't forget to buy some fish and chips on the wharf for the return journey home. Ferrys are cheap and leave regularly www.sydneyferries.info/timetables/manly.php.
The Ferry to manly takes 30 mins the jet Cat 15. Tickets are 12AUD and 15.80AUD return. This is the day you buy a daytripper (but you cant use it on the jet cat!)