The .tmx format is an XML-based format. That means you can parse the files with an XML parser. There are several options for this in Java. Which one you use depends on personal taste.
You might also want to take a look at the other export formats Tiled supports. In one project I found it much easier to use the JSON format. That was because the project was using JSON for other things so I already had a good JSON library and some useful utility functions.