Most information can be found in the JEuclid API Documentation. This document gives a short overview and pointers where to start.
If you program with JEuclid and you need to do more than simple displaying / converting of math, you may be interested in the following
The JEuclid DOM Tree conforms to the MathML Document Object Model Java Binding. This means you can (and should) use the methods defined there to modify the internal tree.