Q:

Writing Calculator class into a "Command Line Calculator" program (Java)

Here is the relevant part of the main program from the assignment: 
public static void main(String [] args) {

        int characters = args.length;
        if (characters < 3) 

            System.out.println("You did not type in a calculation!"); 

        else if (characters % 2 == 0)

            System.out.println("Invalid number of command line parameters."); 

        else {

            Calculathor counter = new Calculathor();
            counter.count(args);
        }
    }
}

I'm only allowed to write the class shown below (Calculator) into the program in the assignment.  I just can't figure out how to get a printable result from the calculation.  
I presume the switch statement is working as intended in receiving the operator from user's input and putting it to use but I need something else to get the actual result. 
class Calculator {

int result;
int i = 0;

    String[] args;

    void count(String[] args) {

    switch (args[i].charAt(i)) {
    case '+': result = Integer.parseInt(args[i]) +
    Integer.parseInt(args[i+2]);
    break;

    case '-': result = Integer.parseInt(args[i]) -
    Integer.parseInt(args[i+2]);
    break;
    }

System.out.println("\nResult of the calculation " + args[0] + " + " + args[2] + " + " + args[4] + " - " + args[6] + " is " + result);

    }
}

A:

Here are some pointers:
Calculathor counter = new Calculathor();

should probably be
Calculator counter = new Calculator();

And, a switch statement is more or less a substitute for if-elseif-else-statements (see the linked tutorial for clarification). 
You probably want to loop over each argument and check if it's a number or an operator.  For example:
for(String arg: args){
    ///Code 
}

or 
for(int i = 0; i < args.length; i++) {
    //Code
}

Within this loop you can have a switch statement that checks if the current arg is an int or an operator.  You could, for example, increment i by more than one to do one summation at each iteration, e.g i+=3 instead of i++ (Warning: Think it through so you don't get an ArrayIndexOutOfBoundsException)
Also, there's probably no need for charAt since each arg is a string of length 1 (I assume).  If you have one big string you probably only want to loop over args[0].