Your Comparator would look like this:

public class GraduationCeremonyComparator implements Comparator<GraduationCeremony> {
    public int compare(GraduationCeremony o1, GraduationCeremony o2) {
        int value1 = o1.campus.compareTo(o2.campus);
        if (value1 == 0) {
            int value2 = o1.faculty.compareTo(o2.faculty);
            if (value2 == 0) {
                return o1.building.compareTo(o2.building);
            } else {
                return value2;
            }
        }
        return value1;
    }
}

Basically it continues comparing each successive attribute of your class whenever the compared attributes so far are equal (== 0).

Use a custom comparator:

Collections.sort(nodeList, new Comparator<DataNode>(){
     public int compare(DataNode o1, DataNode o2){
         if(o1.degree == o2.degree)
             return 0;
         return o1.degree < o2.degree ? -1 : 1;
     }
});

(originally from Ways to sort lists of objects in Java based on multiple fields)

Original working code in this gist

Using Java 8 lambda's (added April 10, 2019)

Java 8 solves this nicely by lambda's (though Guava and Apache Commons might still offer more flexibility):

Collections.sort(reportList, Comparator.comparing(Report::getReportKey)
            .thenComparing(Report::getStudentNumber)
            .thenComparing(Report::getSchool));

Thanks to @gaoagong's answer below.

Note that one advantage here is that the getters are evaluated lazily (eg. getSchool() is only evaluated if relevant).

Messy and convoluted: Sorting by hand

Collections.sort(pizzas, new Comparator<Pizza>() {  
    @Override  
    public int compare(Pizza p1, Pizza p2) {  
        int sizeCmp = p1.size.compareTo(p2.size);  
        if (sizeCmp != 0) {  
            return sizeCmp;  
        }  
        int nrOfToppingsCmp = p1.nrOfToppings.compareTo(p2.nrOfToppings);  
        if (nrOfToppingsCmp != 0) {  
            return nrOfToppingsCmp;  
        }  
        return p1.name.compareTo(p2.name);  
    }  
});  

This requires a lot of typing, maintenance and is error prone. The only advantage is that getters are only invoked when relevant.

The reflective way: Sorting with BeanComparator

ComparatorChain chain = new ComparatorChain(Arrays.asList(
   new BeanComparator("size"), 
   new BeanComparator("nrOfToppings"), 
   new BeanComparator("name")));

Collections.sort(pizzas, chain);  

Obviously this is more concise, but even more error prone as you lose your direct reference to the fields by using Strings instead (no typesafety, auto-refactorings). Now if a field is renamed, the compiler won’t even report a problem. Moreover, because this solution uses reflection, the sorting is much slower.

Getting there: Sorting with Google Guava’s ComparisonChain

Collections.sort(pizzas, new Comparator<Pizza>() {  
    @Override  
    public int compare(Pizza p1, Pizza p2) {  
        return ComparisonChain.start().compare(p1.size, p2.size).compare(p1.nrOfToppings, p2.nrOfToppings).compare(p1.name, p2.name).result();  
        // or in case the fields can be null:  
        /* 
        return ComparisonChain.start() 
           .compare(p1.size, p2.size, Ordering.natural().nullsLast()) 
           .compare(p1.nrOfToppings, p2.nrOfToppings, Ordering.natural().nullsLast()) 
           .compare(p1.name, p2.name, Ordering.natural().nullsLast()) 
           .result(); 
        */  
    }  
});  

This is much better, but requires some boiler plate code for the most common use case: null-values should be valued less by default. For null-fields, you have to provide an extra directive to Guava what to do in that case. This is a flexible mechanism if you want to do something specific, but often you want the default case (ie. 1, a, b, z, null).

And as noted in the comments below, these getters are all evaluated immediately for each comparison.

Sorting with Apache Commons CompareToBuilder

Collections.sort(pizzas, new Comparator<Pizza>() {  
    @Override  
    public int compare(Pizza p1, Pizza p2) {  
        return new CompareToBuilder().append(p1.size, p2.size).append(p1.nrOfToppings, p2.nrOfToppings).append(p1.name, p2.name).toComparison();  
    }  
});  

Like Guava’s ComparisonChain, this library class sorts easily on multiple fields, but also defines default behavior for null values (ie. 1, a, b, z, null). However, you can’t specify anything else either, unless you provide your own Comparator.

Again, as noted in the comments below, these getters are all evaluated immediately for each comparison.

Thus

Ultimately it comes down to flavor and the need for flexibility (Guava’s ComparisonChain) vs. concise code (Apache’s CompareToBuilder).

Bonus method

I found a nice solution that combines multiple comparators in order of priority on CodeReview in a MultiComparator:

class MultiComparator<T> implements Comparator<T> {
    private final List<Comparator<T>> comparators;

    public MultiComparator(List<Comparator<? super T>> comparators) {
        this.comparators = comparators;
    }

    public MultiComparator(Comparator<? super T>... comparators) {
        this(Arrays.asList(comparators));
    }

    public int compare(T o1, T o2) {
        for (Comparator<T> c : comparators) {
            int result = c.compare(o1, o2);
            if (result != 0) {
                return result;
            }
        }
        return 0;
    }

    public static <T> void sort(List<T> list, Comparator<? super T>... comparators) {
        Collections.sort(list, new MultiComparator<T>(comparators));
    }
}

Ofcourse Apache Commons Collections has a util for this already:

ComparatorUtils.chainedComparator(comparatorCollection)

Collections.sort(list, ComparatorUtils.chainedComparator(comparators));

You can use Collections.sort as follows:

private static void order(List<Person> persons) {

    Collections.sort(persons, new Comparator() {

        public int compare(Object o1, Object o2) {

            String x1 = ((Person) o1).getName();
            String x2 = ((Person) o2).getName();
            int sComp = x1.compareTo(x2);

            if (sComp != 0) {
               return sComp;
            } 

            Integer x1 = ((Person) o1).getAge();
            Integer x2 = ((Person) o2).getAge();
            return x1.compareTo(x2);
    }});
}

List<Persons> is now sorted by name, then by age.

String.compareTo "Compares two strings lexicographically" - from the docs.

Collections.sort is a static method in the native Collections library. It does the actual sorting, you just need to provide a Comparator which defines how two elements in your list should be compared: this is achieved by providing your own implementation of the compare method.

As @Rogue has said in the comment you need a reference to an instance of Employer.

In case if all Person instances belong to the same Employer, then you can use it in the keyExtractor function of thenComparing() (alternatively, you can use thenComparingInt()):

List<Person> persons = Arrays.asList(new Person[]{p1, p2, p3, p4});
Employer employer = // initializing the employer

Collections.sort(persons, Comparator.comparing(Person::getAge)
    .thenComparing(Person::getYearsOfEducation)
    .thenComparing(employer::getYearsOfEmployment);

Where employer::getYearsOfEmployment is an equivalent of the following lambda expression:

person -> employer.getYearsOfEmployment(person)

And it should be qualified as a Reference to an Instance Method of a Particular Object