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You can call either a class's constructor or a method in a class or both.
What method in the class do you want to call? Look at the class definition and find the method you want to call.


The...

The compiler can not find a method named: theMethod() in the class: TicTacToe
What method in the class are you trying to call? Check the class definition for the methods that it defines.

That could work.
Did you try it? What happened?

Your terminology is confusing. Classes like JFrame can cause GUI items to appear on the screen as windows.
The source file: TicTacToe.java does not appear. The source file contains the definition...

What method do you want to call? Those classes have several methods in them.
Is there a reference to an instance of the class with that method available in the if statements where you want to call...

Are those classes or methods that you want to call? You need to explain which.
Have instances of those two classes been created? If so where are the variables that point to those instances? If...

You call methods in a class, not programs.
Get a reference to the class that has the method and use it to call the method:
refToClass.theMethod();

Please edit you post and wrap the code in code tags.

if (arg == "Versus Mode")
{
You should use the equals() method to compare Strings.
It would be better to compare the source of the event or...