Thank you everybody for your suggestions (I am VERY appreciative). I have
been reading through both the links, and I think they are helping. I also
took the suggestion of making two different comparators (here I attempted
just the one for X values). Perhaps I am still going about it the wrong way,
but I managed to get a piece of code that finally compiled.

import java.io.*;
import java.util.*;
import java.awt.*;

public class PointCollection2
{
 static ArrayList<Point> this_use_array;
 
 /*Using the method provided in the PS7File class to turn a file into an
ArrayList of points*/
 public static ArrayList<Point> PointCollection(File desired_file)
 {
   PS7File for_this_use = new PS7File(); //creates an object of type PS7File
so that the methods can be called in this class
   
   ArrayList<Point> this_use_array = for_this_use.points_from_file
(desired_file);
   
   return this_use_array; //the ArrayList of points needed for sorting is
created
 }
 
 public static ArrayList<Point> sort(int d)
 {
 Double pee, kyew;
 
 if (d == 0)
 {
   class MyLittlePointComparator extends PS7File.EqComparator implements
Comparator<Point>
  {
      public int compare(Point p, Point q)
      {
        Double pee = p.getX();
        Double kyew = q.getX();
        return (pee).compareTo(kyew);
      }
   }
   Collections.sort(this_use_array, new MyLittlePointComparator());
 }
 return this_use_array;
}
}

I write a tester program that also compiles.
import java.io.*;
import java.util.*;
import java.awt.*;

public class PointCollectionTest
{
 public static void main(String[] arg)
 {
   PointCollection2 tester = new PointCollection2();
   
   File tester_file = new File("C:\\Documents and Settings\\Elizabeth\\My
Documents\\Programming\\Programs\\randompoints.lst");
   
   ArrayList<Point> tester_array = tester.PointCollection(tester_file);
   
   ArrayList<Point> sorted_array = tester.sort(0);
   
   System.out.print(sorted_array);
 }
}

I'm not having much luck when I actually try to implement the program after
compiling.  I get a very nasty red error message in Dr. Java that reads:
NullPointerException:
 at java.util.Collections.sort(Unknown Source)
 at PointCollection2.sort(PointCollection2.java:34)
 at PointCollectionTest.main(PointCollectionTest.java:15)
 at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
 at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
 at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
 at java.lang.reflect.Method.invoke(Unknown Source)

I might have an idea what is wrong. I want to sort the arrayList (here,
this_use_array) made from the file of points with the method PointCollection.
I thought I fixed the problem by declaring this_use_array at the top before
writing any methods, but I guess that doesn't work?

I am not sure how to fix this.