Money class for handling calculations with coins
There is a general purpose guideline - the Single Responsibility Principle. For a given procedure/function you should be able to write a simple statement "This code does X." If you find yourself writing "This code does X and Y." then you should consider breaking the code up into pieces - one piece that does X and one piece that does Y.

The code above does three things - reads input, calculates change, writes output. Those three pieces are candidates for creating separate functions.

I say candidates because there is always a trade-off. When you extract some code into a new function/method then you also have to be able to communicate input to the new function/method as well as for it to communicate back its results. Your code is fairly simple and straightforward as is. Even though it has three different parts and is longer than would be preferred for a single function, splitting it up wouldn't improve it that much while at the same time adding extra complication/overhead in the method calls and returns.

However, that said, if this code became the basis for a more advanced assignment, one thing that you could do would be to create a Change or Payment class something like I have shown below. It encapsulates two parts of the functionality in your code in a simple and direct way that provides a basis for adding additional features.

For example, if you needed to calculate the amount tendered from counts of coins and bills, you could add a function that reads a count of coins tendered and another that calculates the total value.

class Payment {
    int dollars = 0;
    int quarters = 0;
    int dimes = 0;
    int nickels = 0;
    int pennies = 0;

    public payment(int value) {
        int remainder = value;

        dollars = remainder / 100;    
        remainder = remainder % 100;  

        quarters = remainder / 25;  
        remainder = remainder % 25;  

        dimes = remainder / 10;  
        remainder = remainder % 10;

        nickels = remainder / 5;  
        remainder = remainder % 5;  

        pennies = remainder;  
    }

    public writeOutput(PrintStream out) {
        out.println("\t \t " + dollars + " one-dollar bills(s)\n \t \t " 
                             + quarters + " quarter(s)\n \t \t " + dimes + 
                             " dime(s)\n \t \t " + nickels + " nickle(s)\n \t \t " + 
                             pennies + " penn(y/ies)");

    }
}