It's easy to make an incredible mess of this one.  My solution is only 27 lines long.

First, try arguments in the write-up's examples with args.java to be sure you understand the arguments you'll be getting.

Then make the one-argument case work:
    % java eval 7
    7
Have 7 end up in an int called 'value'.

Next, observe that
    java eval 7 + 10
can be thought of as "doing" +10 to the int 'value'.

Continuing, think of
    java 7 + 10 + 3
as
    7
    +10
    +3

Think of the general form of expressions for eval as an initial value followed by zero or more operator & operand pairs.

Once you've got eval working for expressions only involving the + operator, then implement the other operators.