Travelling from Lindau (or any other German town) to XYZ by bus/train

I am trying to figure out how to find transportation options to get from one small German city to another. For example - how can I get from Lindau to Schwangau (to Schongau?, to Augsburg)? Bus? Train? Taxi? Eurolines bus service does not offer the service between these cities. Any advise on how to figure out transportation options in Germany will be greatly appreciated. These cities are just an example. I am planning backpacking trip to Germany, but if I can't find the information on how to plan for the transportation I am in trouble even before starting the trip

Perhaps someone knows site/service where I can enter the names of any two cities and get transportation options? Any advice/help will be greatly appreciated.

Thank you!