Depending on whether this is a classroom assignment or not, you might
look into JavaCC.

JavaCC allows you to define a syntax for a language.  In our usage of
it, we have an application which allows users to include what we call
"expression language" statements.  JavaCC was used to define the syntax
and generate base code for all the various statement types.  We then had
to fill in the internals of many of the resulting classes, and add some
code to others.  But it's not for the faint of heart...

= Steve =

Other posters have already described one approach, of writing  a
parser. If you take this approach, my advice is to keep the language
simple. Also look at ANTLR besides JavaCC, I have used ANTLR in past
for very similar functionality (allowing users to extend) and was quite
happy with it.

A couple other approaches that may be suitable:

1. Define a Java interface that the user has to implement. You can
compile there java code using javac (or the compiler api), load the
class dynamically, instantiate an object and call some method(s) on it.
This is on the lines of plug-in architecture.

2. Embed a javascript engine. I think Java 6 already does this. Can the
functionality the user has to provide be implemented in javascript?