First, make a backup copy of all of the files that are currently running this application under Tomcat. That'll give you a baseline (albeit broken) to return to if your future changes don't work.
Next, make the fix in the .java file and compile it. If your .java file is in the c:\\Documents and Settings\\moffitt\\application_name\\src\\com\\mycompany directory, then you'll want to be in the c:\\Documents and Settings\\moffitt\\application_name\\src directory, and run javac com\\mycompany\\Filename.java. The output of that should be a .class file in the same directory as the .java file. (I'm assuming here that your application does not have an Ant build.xml file, which would likely simplify things.)
Finally, shut down Tomcat, copy the .class file from where it's just been created into exactly where it is inside the Tomcat directory structure, and start the Tomcat back up.