You might consider a direct flight-connection to the Regional Airport Rostock-Laage. However, currently there are a only a few daily connections to Munich and Stuttgart.
If you can't take a direct flight to Rostock-Laage, we recommend flying either via Hamburg or Berlin. The connection via Hamburg is a little bit faster and less complex.
Fly to Hamburg-Airport. There is a train-station located directly at the airport. Take the S1-Train (direction Hamburg Altona) to Hamburg Hauptbahnhof (main station, often abbreviated as "HBf"). The ride on the S1 takes approximately 25 minutes. At Hamburg Hauptbahnhof you can take a direct train-connection (either ICE or RE) to Rostock Hauptbahnhof (the ride takes between 2 and 2.5 hours). Trains to Rostock are leaving at least every two hours.
If you consider travelling via Berlin, you should keep in mind that there are currently two airports in Berlin, Berlin-Schoenefeld (SXF) and Berlin-Tegel (TXL), and that only Berlin-Schoenefeld is connected to the railway-system (S-Trains, and RE/RB-Trains). So flying via Berlin-Schoenefeld (SXF) is strongly advised. For travelling from Berlin-Schoenefeld (SXF) to Rostock by train many connection-variants are possible, but in most cases you have to change trains either at Berlin-Suedkreuz or Berlin Hauptbahnhof. A direct train to Rostock (RE or ICE) is leaving from Berlin Hauptbahnhof approximately every two hours (the ride takes between 2.5 and 3 hours).
Please consider using the Web-Page of the Deutsche Bahn for planning your trip . You can also use it to purchase an online ticket, which you can print and take with you or keep as a PDF on your mobile (smart)-phone. Please avoid the cheap-fare option (called "Sparpreis"). In this case the ticket is valid ONLY for the one particular train-connection specified on the ticket. A "normal" ticket allows you to use any train-connection from your starting point to your destination during a 24 hour window (e.g. in case your plane is late).
From Hamburg take the Autobahn A1 toward Fehmarn-Puttgarden. After about 44 kilometers take the exit 24 onto A20 toward Bad Segeberg and Rostock. After about 114 kilometers take the exit 15 toward Rostock-Südstadt. Follow the signs to the city center.