Public transport in the state Schleswig-Holstein is organized and coordinated by NAH.SH. For information about timetables and prices please visit their website or download their application for mobile devices.
NAH.SH website in English:
http://www.nah.sh/en/

Rail bound public transport in Germany is mainly organized by the Deutsche Bahn.
Deutsche Bahn website: http://www.bahn.de/

In Kiel, there are two ferry lines to cross the Fjord and the Schwentine:
http://www.sfk-kiel.de/en/ferries/fjord
http://www.sfk-kiel.de/en/ferries/schwentine

Kiel is a great city to use a bicycle for transportation.
There are websites for bike sharing, where you can rent bikes with mobile applications.
If you stay for a longer period it might be useful to buy a bike; there a plenty of bike stores in Kiel that sell new and second-hand bicycles.