You can jump on a train to various destinations on the island, including Sassnitz and the Baltic resort of Binz. It costs just over €18 and you can get the ticket from the automatic machines in the station, which are available in English and accept all manner of coins, notes and cards. A couple of tips: Firstly on the way to the island grab a top-deck seat, as otherwise you will miss the view over the Stralsund as the lower tier has its view blocked by metal plates for the most part. Secondly, if you are heading for Binz I would recommend changing trains at Lietzow, if at all possible, as the capital Bergen is pretty functional, and actually quite ugly, whereas Lietzow is out in the country with pleasant views over the lakes.
Stralsund is on the main line to Binz on the island of Ruegen, which passes through Rostock on its way through. It's a very long way away from pretty much anywhere, but thankfully you can get a sleeper train from cities like Munich and Cologne. It takes 3 hours to reach the town by direct regional train from Berlin, and costs about €30.
You can find out about night trains to the town if you can speak a little German via the Nachtzug site:
The town has a big traffic problem. Everyone who wants to go to Rügen has to drive through Stralsund. Quite often you have to wait two hours in traffic jam before entering the town.
However, in town you find numerous parking lots.