String pet = JOptionPane.showInputDialog("Enter …);
instead of two lines like you’ve got it.
Do that for every dialog.

.showInputDialog( 1 arg) or optionally some more args
.showMessageDialog( null, 1 arg ) or optionally some more
the null is does Dialog belong to a JFrame or the Screen.
Normally, we check to see if the input was blank, but it is not required.

but a fun question. (Give points to above dude if you award points)
References :

code was just right ,you needed to add sysout thats it..

Here’s the code
import javax.swing.JOptionPane;

public class WordGame
{

public static void main(String[] args)
{

String name;
name= JOptionPane.showInputDialog("Enter your name");

String age;
age= JOptionPane.showInputDialog("Enter your age");

String city;
city= JOptionPane.showInputDialog("Enter the name of a city");

String college;
college= JOptionPane.showInputDialog("Enter the name of a college");

String profession;
profession= JOptionPane.showInputDialog("Enter profession");

String animal;
animal= JOptionPane.showInputDialog("Enter a type of animal");

String pet;
pet= JOptionPane.showInputDialog("Enter a pet name");

String str="There once was a person named "+ name+
" \n who lived in CITY. At the age of "+age+
", "+ name +" went to college at \n"+ college+" ."+ name
+" graduated and went to work as a \n"+profession+" . Then, "+ name
+" adopted a(n) "+ animal +" \n named "+ pet+
". They both lived happily ever after!";
JOptionPane.showMessageDialog(null, str);
}
}

Cheers:)
References :